Monsters seem to share your line of sight. The easiest way to see this is with goblin rock-throwers. If you have a good perception score they can target you from at least 5 spaces away, but they will never attack you from outside your line of sight, no matter how wretched your perception is. This also has an effect on the barbarian random encounter: if you have legendarily low perception (5 or less) often you wont get shot at that much.

You can also notice this when you have the earth shard equipped. Currently it lets you see through walls, and this seems to change monster behavior. For instance, in the following situation the giant wont move as long as you have the earth shard equipped.