diff --git a/searcharray/postings.py b/searcharray/postings.py
index 9defd6a..5f5bfe1 100644
--- a/searcharray/postings.py
+++ b/searcharray/postings.py
@@ -668,7 +668,7 @@ def positions(self, token: str, key=None) -> List[np.ndarray]:
         posns = self.posns.positions(term_id, key=key)
         return posns
 
-    def and_query(self, tokens: List[str]) -> np.ndarray:
+    def and_query(self, tokens: List[str] | List[List[str]]) -> np.ndarray:
         """Return a mask on the postings array indicating which elements contain all terms."""
         masks = [self.match(term) for term in tokens]
         mask = np.ones(len(self), dtype=bool)
@@ -676,12 +676,10 @@ def and_query(self, tokens: List[str]) -> np.ndarray:
             mask = mask & curr_mask
         return mask
 
-    def or_query(self, tokens: List[str]) -> np.ndarray:
+    def or_query(self, tokens: List[str] | List[List[str]], min_should_match: int = 1) -> np.ndarray:
         """Return a mask on the postings array indicating which elements contain all terms."""
         masks = [self.match(term) for term in tokens]
-        mask = np.ones(len(self), dtype=bool)
-        for curr_mask in masks:
-            mask = mask & curr_mask
+        mask = np.sum(masks, axis=0) >= min_should_match
         return mask
 
     def phrase_freq(self, tokens: List[str], slop=1) -> np.ndarray:
diff --git a/test/test_search.py b/test/test_search.py
new file mode 100644
index 0000000..43a2d4c
--- /dev/null
+++ b/test/test_search.py
@@ -0,0 +1,121 @@
+"""Test postings array search functionality."""
+import pytest
+import numpy as np
+from searcharray.postings import PostingsArray
+from test_utils import w_scenarios
+
+
+@pytest.fixture
+def data():
+    """Return a fixture of your data here that returns an instance of your ExtensionArray."""
+    return PostingsArray.index(["foo bar bar baz", "data2", "data3 bar", "bunny funny wunny"] * 25)
+
+
+def test_match(data):
+    matches = data.match("foo")
+    assert (matches == [True, False, False, False] * 25).all()
+
+
+def test_match_missing_term(data):
+    matches = data.match("not_present")
+    assert (matches == [False, False, False, False] * 25).all()
+
+
+def test_term_freqs(data):
+    matches = data.term_freq("bar")
+    assert (matches == [2, 0, 1, 0] * 25).all()
+
+
+def test_doc_freq(data):
+    doc_freq = data.doc_freq("bar")
+    assert doc_freq == (2 * 25)
+    doc_freq = data.doc_freq("foo")
+    assert doc_freq == 25
+
+
+def test_doc_lengths(data):
+    doc_lengths = data.doc_lengths()
+    assert doc_lengths.shape == (100,)
+    assert (doc_lengths == [4, 1, 2, 3] * 25).all()
+    assert data.avg_doc_length == 2.5
+
+
+def test_bm25_matches_lucene(data):
+    bm25_idf = data.bm25_idf("bar")
+    assert bm25_idf > 0.0
+    bm25 = data.bm25("bar")
+    assert bm25.shape == (100,)
+    assert np.isclose(bm25, [0.37066694, 0., 0.34314217, 0.] * 25).all()
+
+
+and_scenarios = {
+    "base": {
+        "docs": lambda: PostingsArray.index(["foo bar bar baz", "data2", "data3 bar", "bunny funny wunny"] * 25),
+        "keywords": ["foo", "bar"],
+        "expected": [True, False, False, False] * 25,
+    },
+    "no_match": {
+        "docs": lambda: PostingsArray.index(["foo bar bar baz", "data2", "data3 bar", "bunny funny wunny"] * 25),
+        "keywords": ["foo", "data2"],
+        "expected": [False, False, False, False] * 25,
+    },
+    "and_with_phrase": {
+        "docs": lambda: PostingsArray.index(["foo bar bar baz", "data2", "data3 bar", "bunny funny wunny"] * 25),
+        "keywords": [["foo", "bar"], "baz"],
+        "expected": [True, False, False, False] * 25,
+    }
+}
+
+
+@w_scenarios(and_scenarios)
+def test_and_query(data, docs, keywords, expected):
+    docs = docs()
+    matches = data.and_query(keywords)
+    assert (expected == matches).all()
+
+
+or_scenarios = {
+    "base": {
+        "docs": lambda: PostingsArray.index(["foo bar bar baz", "data2", "data3 bar", "bunny funny wunny"] * 25),
+        "keywords": ["foo", "bar"],
+        "expected": [True, False, True, False] * 25,
+        "min_should_match": 1,
+    },
+    "mm_2": {
+        "docs": lambda: PostingsArray.index(["foo bar bar baz", "data2", "data3 bar", "bunny funny wunny"] * 25),
+        "keywords": ["foo", "bar"],
+        "expected": [True, False, False, False] * 25,
+        "min_should_match": 2,
+    },
+    "one_term_match": {
+        "docs": lambda: PostingsArray.index(["foo bar bar baz", "data2", "data3 bar", "bunny funny wunny"] * 25),
+        "keywords": ["foo", "data2"],
+        "expected": [True, True, False, False] * 25,
+        "min_should_match": 1,
+    },
+    "one_term_match_mm2": {
+        "docs": lambda: PostingsArray.index(["foo bar bar baz", "data2", "data3 bar", "bunny funny wunny"] * 25),
+        "keywords": ["foo", "data2"],
+        "expected": [False, False, False, False] * 25,
+        "min_should_match": 2,
+    },
+    "or_with_phrase": {
+        "docs": lambda: PostingsArray.index(["foo bar bar baz", "data2", "data3 bar", "bunny funny wunny"] * 25),
+        "keywords": [["foo", "bar"], "baz"],
+        "expected": [True, False, False, False] * 25,
+        "min_should_match": 1,
+    },
+    "or_with_phrase_mm2": {
+        "docs": lambda: PostingsArray.index(["foo bar bar baz", "data2", "data3 bar", "bunny funny wunny"] * 25),
+        "keywords": [["foo", "bar"], ["bar", "baz"]],
+        "expected": [True, False, False, False] * 25,
+        "min_should_match": 2,
+    }
+}
+
+
+@w_scenarios(or_scenarios)
+def test_or_query(data, docs, keywords, expected, min_should_match):
+    docs = docs()
+    matches = data.or_query(keywords, min_should_match=min_should_match)
+    assert (expected == matches).all()