diff --git a/CHANGELOG.md b/CHANGELOG.md
index 428b546f8c..105179dc02 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -11,12 +11,15 @@ and this project adheres to [Semantic Versioning](http://semver.org/).
 
 - `Pilot.click`/`Pilot.hover` can't use `Screen` as a selector https://github.com/Textualize/textual/issues/3395
 - App exception when a `Tree` is initialized/mounted with `disabled=True` https://github.com/Textualize/textual/issues/3407
+- Fix location of IME and emoji popups https://github.com/Textualize/textual/pull/3408
 - Fixed application freeze when pasting an emoji into an application on Windows https://github.com/Textualize/textual/issues/3178
 - Fixed duplicate option ID handling in the `OptionList` https://github.com/Textualize/textual/issues/3455
 
 ### Added
 
 - `OutOfBounds` exception to be raised by `Pilot` https://github.com/Textualize/textual/pull/3360
+- `TextArea.cursor_screen_offset` property for getting the screen-relative position of the cursor https://github.com/Textualize/textual/pull/3408
+- `Input.cursor_screen_offset` property for getting the screen-relative position of the cursor https://github.com/Textualize/textual/pull/3408
 - Reactive `cell_padding` (and respective parameter) to define horizontal cell padding in data table columns https://github.com/Textualize/textual/issues/3435
 - Added `Input.clear` method https://github.com/Textualize/textual/pull/3430
 - Added `TextArea.SelectionChanged` and `TextArea.Changed` messages https://github.com/Textualize/textual/pull/3442
diff --git a/src/textual/app.py b/src/textual/app.py
index 11baaf7b7c..312daf7415 100644
--- a/src/textual/app.py
+++ b/src/textual/app.py
@@ -53,6 +53,7 @@
 import rich.repr
 from rich import terminal_theme
 from rich.console import Console, RenderableType
+from rich.control import Control
 from rich.protocol import is_renderable
 from rich.segment import Segment, Segments
 from rich.traceback import Traceback
@@ -418,6 +419,12 @@ def __init__(
         self._animate = self._animator.bind(self)
         self.mouse_position = Offset(0, 0)
 
+        self.cursor_position = Offset(0, 0)
+        """The position of the terminal cursor in screen-space.
+
+        This can be set by widgets and is useful for controlling the
+        positioning of OS IME and emoji popup menus."""
+
         self._exception: Exception | None = None
         """The unhandled exception which is leading to the app shutting down,
         or None if the app is still running with no unhandled exceptions."""
@@ -2424,7 +2431,11 @@ def _display(self, screen: Screen, renderable: RenderableType | None) -> None:
                 try:
                     try:
                         if isinstance(renderable, CompositorUpdate):
+                            cursor_x, cursor_y = self.cursor_position
                             terminal_sequence = renderable.render_segments(console)
+                            terminal_sequence += Control.move_to(
+                                cursor_x, cursor_y
+                            ).segment.text
                         else:
                             segments = console.render(renderable)
                             terminal_sequence = console._render_buffer(segments)
@@ -2434,7 +2445,9 @@ def _display(self, screen: Screen, renderable: RenderableType | None) -> None:
                         self._driver.write(terminal_sequence)
                 finally:
                     self._end_update()
+
                 self._driver.flush()
+
         finally:
             self.post_display_hook()
 
diff --git a/src/textual/screen.py b/src/textual/screen.py
index 631dadb4ba..c5404bc05f 100644
--- a/src/textual/screen.py
+++ b/src/textual/screen.py
@@ -515,7 +515,7 @@ def _reset_focus(
                 chosen = candidate
                 break
 
-        # Go with the what was found.
+        # Go with what was found.
         self.set_focus(chosen)
 
     def _update_focus_styles(
diff --git a/src/textual/widgets/_input.py b/src/textual/widgets/_input.py
index c7603297ea..c21afb690e 100644
--- a/src/textual/widgets/_input.py
+++ b/src/textual/widgets/_input.py
@@ -15,7 +15,7 @@
 from .._segment_tools import line_crop
 from ..binding import Binding, BindingType
 from ..events import Blur, Focus, Mount
-from ..geometry import Size
+from ..geometry import Offset, Size
 from ..message import Message
 from ..reactive import reactive
 from ..suggester import Suggester, SuggestionReady
@@ -254,6 +254,7 @@ def __init__(
         super().__init__(name=name, id=id, classes=classes, disabled=disabled)
         if value is not None:
             self.value = value
+
         self.placeholder = placeholder
         self.highlighter = highlighter
         self.password = password
@@ -327,6 +328,14 @@ def _watch_cursor_position(self) -> None:
         else:
             self.view_position = self.view_position
 
+        self.app.cursor_position = self.cursor_screen_offset
+
+    @property
+    def cursor_screen_offset(self) -> Offset:
+        """The offset of the cursor of this input in screen-space. (x, y)/(column, row)"""
+        x, y, _width, _height = self.content_region
+        return Offset(x + self._cursor_offset - self.view_position, y)
+
     async def _watch_value(self, value: str) -> None:
         self._suggestion = ""
         if self.suggester and value:
@@ -425,6 +434,7 @@ def _on_focus(self, _: Focus) -> None:
         self.cursor_position = len(self.value)
         if self.cursor_blink:
             self.blink_timer.resume()
+        self.app.cursor_position = self.cursor_screen_offset
 
     async def _on_key(self, event: events.Key) -> None:
         self._cursor_visible = True
diff --git a/src/textual/widgets/_text_area.py b/src/textual/widgets/_text_area.py
index 2169ea9cc0..daeee49e94 100644
--- a/src/textual/widgets/_text_area.py
+++ b/src/textual/widgets/_text_area.py
@@ -410,6 +410,7 @@ def _watch_selection(self, selection: Selection) -> None:
             if match_row in range(*self._visible_line_indices):
                 self.refresh_lines(match_row)
 
+        self.app.cursor_position = self.cursor_screen_offset
         self.post_message(self.SelectionChanged(selection, self))
 
     def find_matching_bracket(
@@ -660,7 +661,14 @@ def _visible_line_indices(self) -> tuple[int, int]:
         Returns:
             A tuple (top, bottom) indicating the top and bottom visible line indices.
         """
-        return self.scroll_offset.y, self.scroll_offset.y + self.size.height
+        _, scroll_offset_y = self.scroll_offset
+        return scroll_offset_y, scroll_offset_y + self.size.height
+
+    def _watch_scroll_x(self) -> None:
+        self.app.cursor_position = self.cursor_screen_offset
+
+    def _watch_scroll_y(self) -> None:
+        self.app.cursor_position = self.cursor_screen_offset
 
     def load_text(self, text: str) -> None:
         """Load text into the TextArea.
@@ -1043,6 +1051,7 @@ def _on_blur(self, _: events.Blur) -> None:
 
     def _on_focus(self, _: events.Focus) -> None:
         self._restart_blink()
+        self.app.cursor_position = self.cursor_screen_offset
 
     def _toggle_cursor_blink_visible(self) -> None:
         """Toggle visibility of the cursor for the purposes of 'cursor blink'."""
@@ -1257,6 +1266,23 @@ def cursor_location(self, location: Location) -> None:
         """
         self.move_cursor(location, select=not self.selection.is_empty)
 
+    @property
+    def cursor_screen_offset(self) -> Offset:
+        """The offset of the cursor relative to the screen."""
+        cursor_row, cursor_column = self.cursor_location
+        scroll_x, scroll_y = self.scroll_offset
+        region_x, region_y, _width, _height = self.content_region
+
+        offset_x = (
+            region_x
+            + self.get_column_width(cursor_row, cursor_column)
+            - scroll_x
+            + self.gutter_width
+        )
+        offset_y = region_y + cursor_row - scroll_y
+
+        return Offset(offset_x, offset_y)
+
     @property
     def cursor_at_first_line(self) -> bool:
         """True if and only if the cursor is on the first line."""
diff --git a/tests/input/test_input_terminal_cursor.py b/tests/input/test_input_terminal_cursor.py
new file mode 100644
index 0000000000..b956a29846
--- /dev/null
+++ b/tests/input/test_input_terminal_cursor.py
@@ -0,0 +1,28 @@
+from textual.app import App, ComposeResult
+from textual.geometry import Offset
+from textual.widgets import Input
+
+
+class InputApp(App):
+    # Apply padding to ensure gutter accounted for.
+    CSS = "Input { padding: 4 8 }"
+
+    def compose(self) -> ComposeResult:
+        yield Input("こんにちは!")
+
+
+async def test_initial_terminal_cursor_position():
+    app = InputApp()
+    async with app.run_test():
+        # The input is focused so the terminal cursor position should update.
+        assert app.cursor_position == Offset(21, 5)
+
+
+async def test_terminal_cursor_position_update_on_cursor_move():
+    app = InputApp()
+    async with app.run_test():
+        input_widget = app.query_one(Input)
+        input_widget.action_cursor_left()
+        input_widget.action_cursor_left()
+        # We went left over two double-width characters
+        assert app.cursor_position == Offset(17, 5)
diff --git a/tests/text_area/test_selection.py b/tests/text_area/test_selection.py
index d089aecc0f..bbc70e476e 100644
--- a/tests/text_area/test_selection.py
+++ b/tests/text_area/test_selection.py
@@ -18,10 +18,12 @@ def compose(self) -> ComposeResult:
         yield text_area
 
 
-def test_default_selection():
+async def test_default_selection():
     """The cursor starts at (0, 0) in the document."""
-    text_area = TextArea()
-    assert text_area.selection == Selection.cursor((0, 0))
+    app = TextAreaApp()
+    async with app.run_test():
+        text_area = app.query_one(TextArea)
+        assert text_area.selection == Selection.cursor((0, 0))
 
 
 async def test_cursor_location_get():
@@ -294,3 +296,41 @@ async def test_select_line(index, content, expected_selection):
         text_area.select_line(index)
 
         assert text_area.selection == expected_selection
+
+
+async def test_cursor_screen_offset_and_terminal_cursor_position_update():
+    class TextAreaCursorScreenOffset(App):
+        def compose(self) -> ComposeResult:
+            yield TextArea("abc\ndef")
+
+    app = TextAreaCursorScreenOffset()
+    async with app.run_test():
+        text_area = app.query_one(TextArea)
+
+        assert app.cursor_position == (3, 0)
+
+        text_area.cursor_location = (1, 1)
+
+        assert text_area.cursor_screen_offset == (4, 1)
+
+        # Also ensure that this update has been reported back to the app
+        # for the benefit of IME/emoji popups.
+        assert app.cursor_position == (4, 1)
+
+
+async def test_cursor_screen_offset_and_terminal_cursor_position_scrolling():
+    class TextAreaCursorScreenOffset(App):
+        def compose(self) -> ComposeResult:
+            yield TextArea("AB\nAB\nAB\nAB\nAB\nAB\n")
+
+    app = TextAreaCursorScreenOffset()
+    async with app.run_test(size=(80, 2)) as pilot:
+        text_area = app.query_one(TextArea)
+
+        assert app.cursor_position == (3, 0)
+
+        text_area.cursor_location = (5, 0)
+        await pilot.pause()
+
+        assert text_area.cursor_screen_offset == (3, 1)
+        assert app.cursor_position == (3, 1)
diff --git a/tests/text_area/test_text_area_theme.py b/tests/text_area/test_text_area_theme.py
deleted file mode 100644
index e69de29bb2..0000000000