  Hierarchical models of galaxy formation now provide a much closer match to
observations than they did a few years ago. The progress has been achieved by
adjusting the description of baryonic processes such as star formation and
supernova/AGN feedback, while leaving the evolution of the underlying dark
matter (DM) halos the same. Being most results very sensitive to the input
baryonic physics, the ultimate vindication of the hierarchical paradigm should
come from observational tests probing more directly the merging history of DM
halos rather than the history of star formation. Two questions may start
addressing this deeper level: is the predicted halo merging rate consistent
with the observed galaxy merging rate? and, are predicted and observed
evolution of the galaxy mass function consistent with each other. The current
status of these issues is briefly reviewed.

Astrophysics