diff --git a/tests/optimagic/optimization/test_history.py b/tests/optimagic/optimization/test_history.py
index 62ccc0284..9c1493401 100644
--- a/tests/optimagic/optimization/test_history.py
+++ b/tests/optimagic/optimization/test_history.py
@@ -1,5 +1,7 @@
+import numpy as np
 import pytest
 from numpy.testing import assert_array_almost_equal as aaae
+from numpy.testing import assert_array_equal
 
 from optimagic.optimization.history import History, HistoryEntry
 from optimagic.typing import Direction, EvalTask
@@ -8,9 +10,9 @@
 @pytest.fixture
 def history_entries():
     return [
-        HistoryEntry(params=[1, 2, 3], fun=1, time=0.1, task=EvalTask.FUN),
-        HistoryEntry(params=[4, 5, 6], fun=2, time=0.2, task=EvalTask.FUN),
-        HistoryEntry(params=[7, 8, 9], fun=3, time=0.3, task=EvalTask.FUN),
+        HistoryEntry(params={"a": 1, "b": [2, 3]}, fun=1, time=0.1, task=EvalTask.FUN),
+        HistoryEntry(params={"a": 4, "b": [5, 6]}, fun=3, time=0.2, task=EvalTask.FUN),
+        HistoryEntry(params={"a": 7, "b": [8, 9]}, fun=2, time=0.3, task=EvalTask.FUN),
     ]
 
 
@@ -19,21 +21,82 @@ def test_history_add_entry(history_entries):
     for entry in history_entries:
         history.add_entry(entry)
 
-    assert history.params == [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
-    assert history.fun == [1, 2, 3]
+    assert history.direction == Direction.MINIMIZE
+
+    assert history.params == [
+        {"a": 1, "b": [2, 3]},
+        {"a": 4, "b": [5, 6]},
+        {"a": 7, "b": [8, 9]},
+    ]
+    assert history.fun == [1, 3, 2]
     assert history.task == [EvalTask.FUN, EvalTask.FUN, EvalTask.FUN]
     assert history.batches == [0, 1, 2]
-    assert history.direction == Direction.MINIMIZE
     aaae(history.time, [0.0, 0.1, 0.2])
 
+    assert_array_equal(history.fun_array, np.array([1, 3, 2], dtype=np.float64))
+    assert_array_equal(history.monotone_fun, np.array([1, 1, 1], dtype=np.float64))
+    assert_array_equal(
+        history.flat_params_array, np.arange(1, 10, dtype=np.float64).reshape(3, 3)
+    )
+    aaae(history.time_array, np.array([0.0, 0.1, 0.2]))
+
 
 def test_history_add_batch(history_entries):
     history = History(Direction.MAXIMIZE)
     history.add_batch(history_entries)
 
-    assert history.params == [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
-    assert history.fun == [1, 2, 3]
+    assert history.direction == Direction.MAXIMIZE
+
+    assert history.params == [
+        {"a": 1, "b": [2, 3]},
+        {"a": 4, "b": [5, 6]},
+        {"a": 7, "b": [8, 9]},
+    ]
+    assert history.fun == [1, 3, 2]
     assert history.task == [EvalTask.FUN, EvalTask.FUN, EvalTask.FUN]
     assert history.batches == [0, 0, 0]
-    assert history.direction == Direction.MAXIMIZE
     aaae(history.time, [0.0, 0.1, 0.2])
+
+    assert_array_equal(history.fun_array, np.array([1, 3, 2], dtype=np.float64))
+    assert_array_equal(history.monotone_fun, np.array([1, 3, 3], dtype=np.float64))
+    assert_array_equal(
+        history.flat_params_array, np.arange(1, 10, dtype=np.float64).reshape(3, 3)
+    )
+    aaae(history.time_array, np.array([0.0, 0.1, 0.2]))
+
+
+def test_history_from_data():
+    params = [{"a": 1, "b": [2, 3]}, {"a": 4, "b": [5, 6]}, {"a": 7, "b": [8, 9]}]
+    fun = [1, 3, 2]
+    task = [EvalTask.FUN, EvalTask.FUN, EvalTask.FUN]
+    batches = [0, 0, 0]
+    time = [0.0, 0.1, 0.2]
+
+    history = History(
+        direction=Direction.MAXIMIZE,
+        fun=fun,
+        params=params,
+        task=task,
+        batches=batches,
+        time=time,
+    )
+
+    assert history.direction == Direction.MAXIMIZE
+
+    assert history.params == params
+    assert history.fun == fun
+    assert history.task == task
+    assert history.batches == batches
+    aaae(history.time, time)
+
+    assert_array_equal(history.fun_array, np.array(fun, dtype=np.float64))
+    assert_array_equal(history.monotone_fun, np.array([1, 3, 3], dtype=np.float64))
+    assert_array_equal(
+        history.flat_params_array, np.arange(1, 10, dtype=np.float64).reshape(3, 3)
+    )
+    aaae(history.time_array, np.array(time))
+
+
+def test_history_invalid_direction():
+    with pytest.raises(ValueError, match="Invalid direction: 'invalid'. Choose from"):
+        History("invalid")