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.Comment: 36 pages, 6 Figures, submitted to New Astronomy Review
