I've done a few companion quests already, but there are some companions where I didn't get any quests so far. I'm beyond Skyhold and already finished one of the two main quests after that point.
I'm wondering if I missed certain triggers for some companions, or maybe I simply didn't have a high enough approval with them. I'm also wondering how the generic collection quests available for some companions (e.g. Red lyrium for Varric and Warden stuff for Backwall) relate to the actual companion quests. I got the companion quest for Varric before even fulfilling the Red lyrium quests, so I'd assume they are unrelated.
So how do I unlock each companion quest exactly? I'd appreciate reasonably spoiler-free answers, as far as that is possible in this case.