uspavati

1. to put someone to sleep; to get someone to sleep
   Konačno sam uspavala bebu. — I finally got the baby to sleep.
   Ovaj film bi uspavao svakoga. — This film would put anyone to sleep.
2. (of a patient, an animal) to put under; to put down
   Pre operacije su ga uspavali. — They put him under before the operation.
   Veterinar je morao da uspava starog psa. — The vet had to put the old dog down.
3. (of vigilance, feelings) to lull; to dull
   Lepim rečima je uspavao našu sumnju. — He lulled our suspicions with nice words.
4. (uspavati se) to oversleep
   Uspavao sam se i zakasnio na posao. — I overslept and was late for work.

"Uspavati se" usually means "to oversleep" but can also mean "to fall asleep"; the usual verb for "to fall asleep" is zaspati.