In April 2013, a workshop entitled "What Regulates Galaxy Evolution" was held at the Lorentz Center. The aim of the workshop was to bring together the observational and theoretical community working on galaxy evolution, and to discuss in depth of the current problems in the subject, as well as to review the most recent observational constraints. A total of 42 astrophysicists attended the workshop. A significant fraction of the time was devoted to identifying the most interesting "open questions" in the field, and to discuss how progress can be made. This review discusses the four questions (one for each day of the workshop) that, in our opinion, were the focus of the most intense debate. We present each question in its context, and close with a discussion of what future directions should be pursued in order to make progress on these problems.

36 pages, 6 Figures, submitted to New Astronomy Reviews