The fundamental goal of galaxy formation studies is to comprehend how the laws of nature turned a Gaussian random distribution of density fluctuations laid down by inflation into a complex population of galaxies seen at the present day. At this time, this author does not see any convincing evidence that any new physics is needed to explain the phenomena of galaxies 36. The problem is more one of complexity: can we tease out the underlying mechanisms that drive different aspects of galaxy formation and evolution. The key here then is "understanding". One can easily comprehend how a 1 / r2 force works and can, by extrapolation, understand how this force applies to the billions of particles of dark matter in an N-body simulation. However, it is not directly obvious (at least not to this author) how a 1 / r2 force leads to the formation of complex filamentary structures and collapsed virialized objects. Instead, we have developed simplified analytic models (e.g. the Zel'dovich approximation, spherical top-hat collapse models etc.) which explain these phenomena in terms more accessible to the human intellect. It seems that this is what we must strive for in galaxy formation theory - a set of analytic models that we can comprehend and which allow us to understand the physics and a complementary set of precision numerical tools to allow us to determine the quantitative outcomes of that physics (in order to make precision tests of our understanding).
The division of galaxy formation models into N-body/hydro and semi-analytic is rather idealized. In reality there is significant overlap between the two - many semi-analytic models make use of dark matter halo merger trees drawn from N-body simulations while many hydrodynamics simulations include recipes for star formation and feedback which are semi-analytic in nature. It seems most likely that these two techniques will continue to develop and may, in fact, grow less distinguishable, incorporating aspects of each other into each other (once again, yin yang).
Galaxy formation benefits from a wealth of observational data, often to the degree that it is an observationally lead field in which theory plays the role of trying to explain observed phenomena. This deluge of data is unlikely to cease any time soon - we can expect more and higher quality data on local galaxies and also the arrival of usefully sized datasets of galaxies at the highest redshifts. Galaxy formation theory should continue to attempt to develop our comprehension of these observed phenomena but should also strive to move into the regime of making true predictions for as-yet-unobserved regions of parameter space (e.g. the high redshift, z 6, Universe; e.g. Finlator et al. 2010, Lacey et al. 2010). Only in this way can we grow our confidence that we have truly understood the physics of galaxy formation.
36 By "new physics" here I mean modifications to established physical laws, new forces or fields etc. Of course, dark matter and dark energy probably require "new physics" of one type or another, but I will leave those as a problem for cosmology... Back.