dospeti

1. (+ u/na + acc.) to get to; to end up; to reach
   Kako je ovo pismo dospelo u moje ruke? — How did this letter end up in my hands?
   Posle nesreće je dospeo u bolnicu. — After the accident he ended up in hospital.
2. (of a payment, debt) to fall due; to become payable
   Rata kredita je dospela prošle nedelje. — The loan instalment fell due last week.
3. (+ da) to manage; to find time
   Nisam dospeo da ti odgovorim na poruku. — I didn't get around to answering your message.

The imperfective counterpart is dospevati. In the sense "to manage, find time", stići is more common in everyday speech.