To nod off; to fall asleep.
To be sleepy and inactive.
To advance drowsily. (Used especially in the phrase "drowse one's way" ⇒ sleepily make one's way.)
To make heavy with sleepiness or imperfect sleep; to make dull or stupid.
The state of being sleepy and inactive.
To awake.
To awaken somebody.
To become more aware of a real-life situation; to concentrate on the matter in hand.