When does the active quests log update?

[Mummelpuffin]

I finished a little fetch quest for someone in a shop but the quest is just sitting there in the log as if it isn't finished. I got the gold from the questgiver, can't even talk to them anymore, but there it sits still.

[Jay_H]

Some quests have a delay to them, since in classic NPCs would disappear when the quest ends. What quest is it?

[Ommamar]

There is also multiple steps and people you have to speak to complete the quest chain, it seems like if you go directly to the item needed in the quest it doesn't complete until you have followed the chain of people involved in the quest. Or it could be the case Jay_H is talking about where there is a delay built into some of the quests.

[Firebrand]

Sometimes quests will move to completed immediately, sometimes after. For example, I was confused during the Daedric Quest for Oghma Infinium, because I had already read the book and the quest was not yet marked completed. Then I fast travelled to Daggerfall, and -voilà- the quest completed itself