diff --git a/src/level.rs b/src/level.rs
index 604d59a..e72a3e9 100644
--- a/src/level.rs
+++ b/src/level.rs
@@ -101,12 +101,18 @@ impl DungeonLevel {
         level.exits
     }
 
-    /// Draws a level on the display window.
-    pub fn draw(&self, win: &Window) {
+    /// Draws a level on the display window. Draws only the cells for
+    /// which `filter` returns true; use `|_| true` to draw the whole
+    /// level.
+    pub fn draw(&self, win: &Window, filter: impl Fn((i32, i32)) -> bool) {
         for y in 0..LEVEL_SIZE.1 {
             win.mv(y as _, 0);
             for x in 0..LEVEL_SIZE.0 {
-                win.addch(self.render_tile(x, y));
+                win.addch(if filter((x as _, y as _)) {
+                    self.render_tile(x, y)
+                } else {
+                    ' '
+                });
             }
         }
     }
diff --git a/src/main.rs b/src/main.rs
index 163077c..991808f 100644
--- a/src/main.rs
+++ b/src/main.rs
@@ -15,6 +15,7 @@ mod player;
 mod rooms;
 mod systems;
 mod util;
+mod visibility;
 
 fn main() {
     let mut world = World::new();
diff --git a/src/player.rs b/src/player.rs
index 786115a..053ad1b 100644
--- a/src/player.rs
+++ b/src/player.rs
@@ -7,6 +7,7 @@ use crate::{
     components::{CharRender, MobAction, Mobile, Player, Position},
     level::DungeonLevel,
     quit,
+    visibility::{visible, CellVisibility, Lighting},
 };
 
 /// Runs a player turn on the ECS, using the given `screen` for input
@@ -85,9 +86,32 @@ fn possible(ecs: &World, action: &MobAction) -> bool {
 
 /// Renders the state of the world onto the screen.
 fn render_screen(ecs: &mut World, screen: &mut Window) {
+    // Calculate the player's position.
+    let plrs = ecs.read_storage::<Player>();
+    let pos = ecs.read_storage::<Position>();
+    let (_plr, player_pos) = (&plrs, &pos)
+        .join()
+        .next()
+        .expect("Player must have a position");
+
     // Draw the base level.
     let level = ecs.fetch::<DungeonLevel>();
-    level.draw(screen);
+    level.draw(screen, |cell| {
+        visible(
+            (player_pos.x, player_pos.y),
+            cell,
+            Some(10),
+            |(x, y)| {
+                if level.tile(x, y).is_navigable() {
+                    CellVisibility::Transparent
+                } else {
+                    CellVisibility::Blocking
+                }
+            },
+            // Level is fully lit for now.
+            |(_x, _y)| Lighting::Lit,
+        )
+    });
 
     // Draw all renderable entities.
     let renderables = ecs.read_storage::<CharRender>();
@@ -97,10 +121,7 @@ fn render_screen(ecs: &mut World, screen: &mut Window) {
     }
 
     // Leave the cursor on the player's position.
-    let plrs = ecs.read_storage::<Player>();
-    let pos = ecs.read_storage::<Position>();
-    let (_plr, pos) = (&plrs, &pos).join().next().unwrap();
-    screen.mv(pos.y, pos.x);
+    screen.mv(player_pos.y, player_pos.x);
 
     screen.refresh();
 }
diff --git a/src/visibility.rs b/src/visibility.rs
new file mode 100644
index 0000000..dd79990
--- /dev/null
+++ b/src/visibility.rs
@@ -0,0 +1,89 @@
+//! Code for determining which cells the player and monsters can see.
+
+/// The light transmission properties of a cell in the world.
+#[derive(Debug, PartialEq)]
+pub enum CellVisibility {
+    /// This cell allows light to pass through: monsters can see
+    /// through this cell as if it is air.
+    Transparent,
+
+    /// This cell blocks all light.
+    Blocking,
+}
+
+/// How well-lit a cell is.
+#[derive(Debug, PartialEq)]
+pub enum Lighting {
+    /// Monsters can only see in this cell if the cell is immediately
+    /// adjacent to the monster.
+    Dark,
+
+    /// Monsters can see in this cell from far away.
+    Lit,
+}
+
+/// Calculates whether a monster standing at `origin` can see the
+/// contents of cell `cell`. We assume the monster can see `radius`
+/// cells away at best (None for unlimited range), that `cell_map`
+/// represents whether a cell transmits light, and that `light_map`
+/// represents how well-lit a cell is.
+pub fn visible(
+    origin: (i32, i32),
+    cell: (i32, i32),
+    radius: Option<i32>,
+    cell_map: impl Fn((i32, i32)) -> CellVisibility,
+    light_map: impl Fn((i32, i32)) -> Lighting,
+) -> bool {
+    let dx = cell.0 - origin.0;
+    let dy = cell.1 - origin.1;
+
+    radius
+        .map(|radius| dx * dx + dy * dy < radius * radius)
+        .unwrap_or(true)
+        && (light_map(cell) == Lighting::Lit)
+        && (line(origin, cell).all(|tile| cell_map(tile) == CellVisibility::Transparent))
+}
+
+/// Constructs an iterator over the cells in a straight line from
+/// `start` to `end`. The line will include `start`, but not `end`.
+fn line(start: (i32, i32), end: (i32, i32)) -> Box<dyn Iterator<Item = (i32, i32)>> {
+    // We could use a dedicated iterator type here eventually and
+    // avoid the `Box` allocations, but I'm gonna assume it's not a
+    // significant problem until proven otherwise.
+
+    let dx = end.0 - start.0;
+    let dy = end.1 - start.1;
+
+    // Transform the world so we're working from left to right, with
+    // slope magnitude less than 1.
+    if dx.abs() < dy.abs() {
+        Box::new(line((start.1, start.0), (end.1, end.0)).map(|(x, y)| (y, x)))
+    } else if dx < 0 {
+        Box::new(line((-start.0, start.1), (-end.0, end.1)).map(|(x, y)| (-x, y)))
+    } else {
+        // Move the destination over by 0.5 cells on each axis, to
+        // navigate to the corner rather than the center of the target
+        // cell. It's weird but it makes things work way better.
+        let dx = dx as f64 - 0.5;
+        let dy = if dy > 0 {
+            dy as f64 - 0.5
+        } else if dy < 0 {
+            dy as f64 + 0.5
+        } else {
+            dy as f64
+        };
+
+        // Now use float math to step along the line, one cell at a
+        // time.
+        let slope = dy as f64 / dx as f64;
+        Box::new(
+            std::iter::successors(Some((start.0, start.1 as f64)), move |&(x, y)| {
+                Some((x + 1, y + slope))
+            })
+            // Add 0.5 here to round to nearest rather than rounding
+            // towards zero (eliminates some bias).
+            .map(|(x, y)| (x, (y + 0.5) as i32))
+            .take_while(move |(x, _y)| x < &end.0),
+        )
+    }
+}