  The formation of the first galaxies at redshifts z ~ 10-15 signaled the
transition from the simple initial state of the universe to one of ever
increasing complexity. We here review recent progress in understanding their
assembly process with numerical simulations, starting with cosmological initial
conditions and modelling the detailed physics of star formation. In this
context we emphasize the importance and influence of selecting appropriate
initial conditions for the star formation process. We revisit the notion of a
critical metallicity resulting in the transition from primordial to present-day
initial mass functions and highlight its dependence on additional cooling
mechanisms and the exact initial conditions. We also review recent work on the
ability of dust cooling to provide the transition to present-day low-mass star
formation. In particular, we highlight the extreme conditions under which this
transition mechanism occurs, with violent fragmentation in dense gas resulting
in tightly packed clusters.
