Let us now summarize the most important unsolved questions in galaxy formation, at small and high mass scales, respectively:
Alongside with the excessive predicted numbers of dwarf galaxies, there is a problem with their inner dark matter density profiles: observations show that they have a core , whereas simulations generally predict a cusp . Moreover, another aspect of the "missing satellite problem"  is the so-called too-big-to-fail problem : the dwarf spheroidal galaxies of the Milky Way live in dark matter haloes which are less concentrated than expected from N-body simulations. Several solutions have been proposed, amongst them modifications of dark matter via self-interactions  or an Einasto-like density profile for satellite galaxies combined with a mass of 8.1011 M for the total mass of the MWG [153, 154]. Probably both of these problems could be solved by simply invoking appropriate feedback mechanisms. Supernovae feedback is able to lower the dwarf central densities ,  but cannot apparently resolve the too-big-to-fail problem . One could perhaps invoke feedback by IMBH to resolve the latter problem: these most likely form ubiquitously in subhalos if IMBH are the building blocks of SMBH, as is commonly assumed in some scenarios of SMBH formation.
How are bulgeless thin disk galaxies formed? This type of galaxy has been observed to be common , while numerical simulations produce galaxies with thick disks and bulges. One appealing solution involves SN feedback, which can drive a galactic fountain that feeds the bulge: this mechanism of redistribution of angular momentum can solve the bulgeless problem . Another proposal includes energy from massive stars as well as SNe . An inevitable consequence of supernova or radiation feedback on dust is likely to be a thick disk. Whether these ideas can be reconciled with observations of spiral galaxies at low z is not clear.
Why is star formation so inefficient with regard to the total baryon reservoir? There is a serious shortfall of baryons in typical galaxies by 50% or more . Baryons are lacking on larger scales too, such as groups and even clusters . The circumgalactic environment may provide the reservoir where the bulk of the baryons reside although this is far from clear, in part because ejected baryons are enriched and cool rapidly in this environment, hence begging the question of what keeps them out. Recirculation mechanisms such as galactic fountains actually bring gas into the disk, indeed these supernova-driven phenomena help explain the current star formation rate in galaxies like the MWG .
Finally, the massive galaxies predicted today are generally too many and too blue. The simulated evolution of the galaxy luminosity function contradicts the data, either at high or at low redshift. For example, in order to match the rest-frame K-band luminosity function of galaxies, reference  used semi-analytic models, including asymptotic giant branch stars in the stellar populations, which result in a more rapid reddening time-scale: in this case , however, there are too many blue galaxies predicted at z ~ 0.5.
ADC and ID thank the Italian INFN for the financial support during the "New Horizons for Observational Cosmology" courses. ADC thanks the MICINN (Spain) for the financial support through the grant AYA2009-13875-C03-02 and the MINECO grant AYA2012-31101 and the MultiDark project, grant CSD2009-00064. The research of JS has been supported at IAP by the ERC project 267117 (DARK) hosted by Université Pierre et Marie Curie - Paris 6 and at JHU by NSF grant OIA-1124403.