The knowledge of compact stellar remnants, neutron stars and black holes, has greatly expanded in recent years. Many of the dogmas of the past were refuted and we face a new era in which the pieces of the puzzle are difficult to fit, but on the other hand many opportunities to contribute appear. I shall discuss in this seminar some of the latter, including the masses and mass distribution of both objects, their birth in stellar collapses and other events, and related topics.