Our theory of galaxy formation is gradually becoming more and more complete, but it is clear that large gaps in our understanding remain. This is, perhaps, not suprising - galaxy formation incorporates a wide array of physical processes, many of which we can currently observe the consequences of only indirectly. Most of the physics of galaxy formation is inherently nonlinear, making it difficult to obtain accurate solutions. Finally, what we observe from galaxies is usually several steps removed from the underlying physical properties (mass, density etc.) that we would ideally like to know about. Despite all of these difficulties, rapid progress is being made. The next decade should see this trend continuing via a combination of ever better observational datasets (both low and high redshift) and the continued development of novel theoretical tools.
The author acknowledges the support of the Gordon & Betty Moore Foundation. This work has benefited greatly from discussions with the Durham galaxy formation Group (Carlos Frenk, Shaun Cole, Richard Bower, Carlton Baugh, Cedric Lacey, Martin Stringer, Andreea Font and John Helly) and with Juna Kollmeier, Alyson Brooks, Annika Peter, Brant Robertson, TJ Cox, Dan Grin, Laura Book and Elisabeth Krause. The author would particularly like to thank Carlos Frenk for carefully reading through this manuscript and the anonymous referee for numerous valuable suggestions.