diff --git a/sentience/query.py b/sentience/query.py
index 8ab2c32..b835ac5 100644
--- a/sentience/query.py
+++ b/sentience/query.py
@@ -16,33 +16,121 @@ def parse_selector(selector: str) -> Dict[str, Any]:
         "role=textbox name~'email'"
         "clickable=true role=link"
         "role!=link"
+        "importance>500"
+        "text^='Sign'"
+        "text$='in'"
     """
     query: Dict[str, Any] = {}
     
-    # Match patterns like: key=value, key~'value', key!="value"
-    # This regex matches: key, operator (=, ~, !=), and value (quoted or unquoted)
-    pattern = r'(\w+)([=~!]+)((?:\'[^\']+\'|\"[^\"]+\"|[^\s]+))'
+    # Match patterns like: key=value, key~'value', key!="value", key>123, key^='prefix', key$='suffix'
+    # Updated regex to support: =, !=, ~, ^=, $=, >, >=, <, <=
+    # Supports dot notation: attr.id, css.color
+    # Note: Handle ^= and $= first (before single char operators) to avoid regex conflicts
+    # Pattern matches: key, operator (including ^= and $=), and value (quoted or unquoted)
+    pattern = r'([\w.]+)(\^=|\$=|>=|<=|!=|[=~<>])((?:\'[^\']+\'|\"[^\"]+\"|[^\s]+))'
     matches = re.findall(pattern, selector)
     
     for key, op, value in matches:
         # Remove quotes from value
         value = value.strip().strip('"\'')
         
+        # Handle numeric comparisons
+        is_numeric = False
+        try:
+            numeric_value = float(value)
+            is_numeric = True
+        except ValueError:
+            pass
+        
         if op == '!=':
             if key == "role":
                 query["role_exclude"] = value
             elif key == "clickable":
                 query["clickable"] = False
+            elif key == "visible":
+                query["visible"] = False
         elif op == '~':
+            # Substring match (case-insensitive)
             if key == "text" or key == "name":
                 query["text_contains"] = value
+        elif op == '^=':
+            # Prefix match
+            if key == "text" or key == "name":
+                query["text_prefix"] = value
+        elif op == '$=':
+            # Suffix match
+            if key == "text" or key == "name":
+                query["text_suffix"] = value
+        elif op == '>':
+            # Greater than
+            if is_numeric:
+                if key == "importance":
+                    query["importance_min"] = numeric_value + 0.0001  # Exclusive
+                elif key.startswith("bbox."):
+                    query[f"{key}_min"] = numeric_value + 0.0001
+                elif key == "z_index":
+                    query["z_index_min"] = numeric_value + 0.0001
+            elif key.startswith("attr.") or key.startswith("css."):
+                query[f"{key}_gt"] = value
+        elif op == '>=':
+            # Greater than or equal
+            if is_numeric:
+                if key == "importance":
+                    query["importance_min"] = numeric_value
+                elif key.startswith("bbox."):
+                    query[f"{key}_min"] = numeric_value
+                elif key == "z_index":
+                    query["z_index_min"] = numeric_value
+            elif key.startswith("attr.") or key.startswith("css."):
+                query[f"{key}_gte"] = value
+        elif op == '<':
+            # Less than
+            if is_numeric:
+                if key == "importance":
+                    query["importance_max"] = numeric_value - 0.0001  # Exclusive
+                elif key.startswith("bbox."):
+                    query[f"{key}_max"] = numeric_value - 0.0001
+                elif key == "z_index":
+                    query["z_index_max"] = numeric_value - 0.0001
+            elif key.startswith("attr.") or key.startswith("css."):
+                query[f"{key}_lt"] = value
+        elif op == '<=':
+            # Less than or equal
+            if is_numeric:
+                if key == "importance":
+                    query["importance_max"] = numeric_value
+                elif key.startswith("bbox."):
+                    query[f"{key}_max"] = numeric_value
+                elif key == "z_index":
+                    query["z_index_max"] = numeric_value
+            elif key.startswith("attr.") or key.startswith("css."):
+                query[f"{key}_lte"] = value
         elif op == '=':
+            # Exact match
             if key == "role":
                 query["role"] = value
             elif key == "clickable":
                 query["clickable"] = value.lower() == "true"
+            elif key == "visible":
+                query["visible"] = value.lower() == "true"
+            elif key == "tag":
+                query["tag"] = value
             elif key == "name" or key == "text":
                 query["text"] = value
+            elif key == "importance" and is_numeric:
+                query["importance"] = numeric_value
+            elif key.startswith("attr."):
+                # Dot notation for attributes: attr.id="submit-btn"
+                attr_key = key[5:]  # Remove "attr." prefix
+                if "attr" not in query:
+                    query["attr"] = {}
+                query["attr"][attr_key] = value
+            elif key.startswith("css."):
+                # Dot notation for CSS: css.color="red"
+                css_key = key[4:]  # Remove "css." prefix
+                if "css" not in query:
+                    query["css"] = {}
+                query["css"][css_key] = value
     
     return query
 
@@ -65,6 +153,18 @@ def match_element(element: Element, query: Dict[str, Any]) -> bool:
         if element.visual_cues.is_clickable != query["clickable"]:
             return False
     
+    # Visible (using in_viewport and !is_occluded)
+    if "visible" in query:
+        is_visible = element.in_viewport and not element.is_occluded
+        if is_visible != query["visible"]:
+            return False
+    
+    # Tag (not yet in Element model, but prepare for future)
+    if "tag" in query:
+        # For now, this will always fail since tag is not in Element model
+        # This is a placeholder for future implementation
+        pass
+    
     # Text exact match
     if "text" in query:
         if not element.text or element.text != query["text"]:
@@ -77,6 +177,87 @@ def match_element(element: Element, query: Dict[str, Any]) -> bool:
         if query["text_contains"].lower() not in element.text.lower():
             return False
     
+    # Text prefix match
+    if "text_prefix" in query:
+        if not element.text:
+            return False
+        if not element.text.lower().startswith(query["text_prefix"].lower()):
+            return False
+    
+    # Text suffix match
+    if "text_suffix" in query:
+        if not element.text:
+            return False
+        if not element.text.lower().endswith(query["text_suffix"].lower()):
+            return False
+    
+    # Importance filtering
+    if "importance" in query:
+        if element.importance != query["importance"]:
+            return False
+    if "importance_min" in query:
+        if element.importance < query["importance_min"]:
+            return False
+    if "importance_max" in query:
+        if element.importance > query["importance_max"]:
+            return False
+    
+    # BBox filtering (spatial)
+    if "bbox.x_min" in query:
+        if element.bbox.x < query["bbox.x_min"]:
+            return False
+    if "bbox.x_max" in query:
+        if element.bbox.x > query["bbox.x_max"]:
+            return False
+    if "bbox.y_min" in query:
+        if element.bbox.y < query["bbox.y_min"]:
+            return False
+    if "bbox.y_max" in query:
+        if element.bbox.y > query["bbox.y_max"]:
+            return False
+    if "bbox.width_min" in query:
+        if element.bbox.width < query["bbox.width_min"]:
+            return False
+    if "bbox.width_max" in query:
+        if element.bbox.width > query["bbox.width_max"]:
+            return False
+    if "bbox.height_min" in query:
+        if element.bbox.height < query["bbox.height_min"]:
+            return False
+    if "bbox.height_max" in query:
+        if element.bbox.height > query["bbox.height_max"]:
+            return False
+    
+    # Z-index filtering
+    if "z_index_min" in query:
+        if element.z_index < query["z_index_min"]:
+            return False
+    if "z_index_max" in query:
+        if element.z_index > query["z_index_max"]:
+            return False
+    
+    # In viewport filtering
+    if "in_viewport" in query:
+        if element.in_viewport != query["in_viewport"]:
+            return False
+    
+    # Occlusion filtering
+    if "is_occluded" in query:
+        if element.is_occluded != query["is_occluded"]:
+            return False
+    
+    # Attribute filtering (dot notation: attr.id="submit-btn")
+    if "attr" in query:
+        # This requires DOM access, which is not available in the Element model
+        # This is a placeholder for future implementation when we add DOM access
+        pass
+    
+    # CSS property filtering (dot notation: css.color="red")
+    if "css" in query:
+        # This requires DOM access, which is not available in the Element model
+        # This is a placeholder for future implementation when we add DOM access
+        pass
+    
     return True
 
 
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diff --git a/tests/test_query.py b/tests/test_query.py
index 18da363..b7b9545 100644
--- a/tests/test_query.py
+++ b/tests/test_query.py
@@ -2,7 +2,6 @@
 Tests for query engine
 """
 
-import pytest
 from sentience import SentienceBrowser, snapshot, query, find
 from sentience.query import parse_selector, match_element
 from sentience.models import Element, BBox, VisualCues
@@ -30,6 +29,39 @@ def test_parse_selector():
     # Negation
     q = parse_selector("role!=link")
     assert q["role_exclude"] == "link"
+    
+    # New operators: prefix and suffix
+    q = parse_selector("text^='Sign'")
+    assert q["text_prefix"] == "Sign"
+    
+    q = parse_selector("text$='in'")
+    assert q["text_suffix"] == "in"
+    
+    # Numeric comparisons: importance
+    q = parse_selector("importance>500")
+    assert "importance_min" in q
+    assert q["importance_min"] > 500
+    
+    q = parse_selector("importance>=500")
+    assert q["importance_min"] == 500
+    
+    q = parse_selector("importance<1000")
+    assert "importance_max" in q
+    assert q["importance_max"] < 1000
+    
+    q = parse_selector("importance<=1000")
+    assert q["importance_max"] == 1000
+    
+    # Visible field
+    q = parse_selector("visible=true")
+    assert q["visible"] is True
+    
+    q = parse_selector("visible=false")
+    assert q["visible"] is False
+    
+    # Tag field (placeholder for future)
+    q = parse_selector("tag=button")
+    assert q["tag"] == "button"
 
 
 def test_match_element():
@@ -41,6 +73,9 @@ def test_match_element():
         importance=100,
         bbox=BBox(x=0, y=0, width=100, height=40),
         visual_cues=VisualCues(is_primary=True, is_clickable=True),
+        in_viewport=True,
+        is_occluded=False,
+        z_index=10,
     )
     
     # Role match
@@ -51,9 +86,71 @@ def test_match_element():
     assert match_element(element, {"text_contains": "Sign"}) is True
     assert match_element(element, {"text_contains": "Logout"}) is False
     
+    # Text prefix
+    assert match_element(element, {"text_prefix": "Sign"}) is True
+    assert match_element(element, {"text_prefix": "Login"}) is False
+    
+    # Text suffix
+    assert match_element(element, {"text_suffix": "In"}) is True
+    assert match_element(element, {"text_suffix": "Out"}) is False
+    
     # Clickable
     assert match_element(element, {"clickable": True}) is True
     assert match_element(element, {"clickable": False}) is False
+    
+    # Visible (using in_viewport and !is_occluded)
+    assert match_element(element, {"visible": True}) is True
+    element_occluded = Element(
+        id=2,
+        role="button",
+        text="Hidden",
+        importance=50,
+        bbox=BBox(x=0, y=0, width=100, height=40),
+        visual_cues=VisualCues(is_primary=False, is_clickable=True),
+        in_viewport=True,
+        is_occluded=True,
+        z_index=5,
+    )
+    assert match_element(element_occluded, {"visible": True}) is False
+    assert match_element(element_occluded, {"visible": False}) is True
+    
+    # Importance filtering
+    assert match_element(element, {"importance_min": 50}) is True
+    assert match_element(element, {"importance_min": 150}) is False
+    assert match_element(element, {"importance_max": 150}) is True
+    assert match_element(element, {"importance_max": 50}) is False
+    
+    # BBox filtering
+    assert match_element(element, {"bbox.x_min": -10}) is True
+    assert match_element(element, {"bbox.x_min": 10}) is False
+    assert match_element(element, {"bbox.width_min": 50}) is True
+    assert match_element(element, {"bbox.width_min": 150}) is False
+    
+    # Z-index filtering
+    assert match_element(element, {"z_index_min": 5}) is True
+    assert match_element(element, {"z_index_min": 15}) is False
+    assert match_element(element, {"z_index_max": 15}) is True
+    assert match_element(element, {"z_index_max": 5}) is False
+    
+    # In viewport filtering
+    assert match_element(element, {"in_viewport": True}) is True
+    element_off_screen = Element(
+        id=3,
+        role="button",
+        text="Off Screen",
+        importance=50,
+        bbox=BBox(x=0, y=0, width=100, height=40),
+        visual_cues=VisualCues(is_primary=False, is_clickable=True),
+        in_viewport=False,
+        is_occluded=False,
+        z_index=5,
+    )
+    assert match_element(element_off_screen, {"in_viewport": False}) is True
+    assert match_element(element_off_screen, {"in_viewport": True}) is False
+    
+    # Occlusion filtering
+    assert match_element(element, {"is_occluded": False}) is True
+    assert match_element(element_occluded, {"is_occluded": True}) is True
 
 
 def test_query_integration():
@@ -89,3 +186,88 @@ def test_find_integration():
             assert link.role == "link"
             assert link.id >= 0
 
+
+def test_query_advanced_operators():
+    """Test advanced query operators"""
+    # Create test elements
+    elements = [
+        Element(
+            id=1,
+            role="button",
+            text="Sign In",
+            importance=1000,
+            bbox=BBox(x=10, y=20, width=100, height=40),
+            visual_cues=VisualCues(is_primary=True, is_clickable=True),
+            in_viewport=True,
+            is_occluded=False,
+            z_index=10,
+        ),
+        Element(
+            id=2,
+            role="button",
+            text="Sign Out",
+            importance=500,
+            bbox=BBox(x=120, y=20, width=100, height=40),
+            visual_cues=VisualCues(is_primary=False, is_clickable=True),
+            in_viewport=True,
+            is_occluded=False,
+            z_index=5,
+        ),
+        Element(
+            id=3,
+            role="link",
+            text="More information",
+            importance=200,
+            bbox=BBox(x=10, y=70, width=150, height=20),
+            visual_cues=VisualCues(is_primary=False, is_clickable=True),
+            in_viewport=True,
+            is_occluded=False,
+            z_index=1,
+        ),
+    ]
+    
+    from sentience.models import Snapshot
+    snap = Snapshot(
+        status="success",
+        url="https://example.com",
+        elements=elements,
+    )
+    
+    # Test importance filtering
+    high_importance = query(snap, "importance>500")
+    assert len(high_importance) == 1
+    assert high_importance[0].id == 1
+    
+    low_importance = query(snap, "importance<300")
+    assert len(low_importance) == 1
+    assert low_importance[0].id == 3
+    
+    # Test prefix matching
+    sign_prefix = query(snap, "text^='Sign'")
+    assert len(sign_prefix) == 2
+    assert all("Sign" in el.text for el in sign_prefix)
+    
+    # Test suffix matching
+    in_suffix = query(snap, "text$='In'")
+    assert len(in_suffix) == 1
+    assert in_suffix[0].text == "Sign In"
+    
+    # Test BBox filtering
+    right_side = query(snap, "bbox.x>100")
+    assert len(right_side) == 1
+    assert right_side[0].id == 2
+    
+    # Test combined queries
+    combined = query(snap, "role=button importance>500")
+    assert len(combined) == 1
+    assert combined[0].id == 1
+    
+    # Test visible filtering
+    visible = query(snap, "visible=true")
+    assert len(visible) == 3  # All are visible
+    
+    # Test z-index filtering
+    high_z = query(snap, "z_index>5")
+    assert len(high_z) == 1
+    assert high_z[0].id == 1
+