What is the issue with SN1987A neutrinos?

What did we learn out of SN1987A neutrino observations? What do we still need for a full understanding? We select important issues debated in the literature on SN1987A. We focus the discussion mostly on the relevance of certain data features; on the role of detailed statistical analyses of the data; on the astrophysics of the neutrino emission process; on the effects of oscillations and of neutrino masses. We attempt to clearly identify those issues that are still open.