l'imparfait vs conditionel passé

Just to add to Maarten's answer:

Here is the difference between the two sentence:

Il devait faire qqc. -- He was supposed to do something.
Il aurait dû faire qqc. -- He should have done something.

Sebastian,

 a link to recent response from Céline. 

Imparfait expresses the sense of a reproach that you were supposed to have done something, but not necessarily with any sense that something negative resulted because you didn’t.

The conditional passé conveys a stronger negative sense - because you didn’t do what you should have, look at what happened !

 https://progress.lawlessfrench.com/questions/view/the-difference-between-devoir-in-le-conditionnel-passe-and-l-imparfait