The book collects a series of articles to review the advances that have been made in the field of gravitational collapse in general relativity and alternative theories of gravity in the past few years. Many approaches to black hole and singularity formation in general relativity and beyond have been proposed over the last few decades. The importance of collapse models is that they provide natural thought experiments where to test the behavior and properties of a variety of approaches to general relativity and its implications for ultra-compact objects in the universe.