In this survey, the author collects and presents several of his recent results and joint works on monomorphism categories, covering various topics in representation theory. We try to show that how one can approach the monomorphism categories via functor categories. In the representation-finite case, we are essentially dealing with module categories, so well-understood knowledge from module categories can be transferred to monomorphism categories. In particular, this approach is effective for developing covering theory for monomorphism categories. The results in Section~3, which provide various equivalences between the monomorphism category and the category of finitely presented covariant functors, are taken from an unpublished paper by the author.
Rasool Hafezi (Sun,) studied this question.