Dovere

The present indicative forms of dovere translate as "owe":

Gli devo la mia gratitudine. (I owe him my gratitude.)
Ti devo venti dollari. (I owe you twenty dollars.)

In the conditional tenses, however, dovere carries the meaning "should" or "ought to." For example:

Dovrei finire i compiti di scuola a tempo. (I should/ought to finish my homework on time.)
Avrei dovuto telefonarle immediatamente. (I should have/ought to have telephoned her immediately.)