I review some recent developments in attempting to reconcile
the observed galaxy population with numerical models of structure formation in
the 'LCDM' concordance cosmology. Focussing on behaviour of dwarf galaxies, I
describe the infamous 'cusp-core' dichotomy -- a long-standing challenge to the
LCDM picture on small scales -- and use toy models to show how it is resolved
in recent numerical simulations (Pontzen & Governato 2012). I then discuss
the current observational status of this picture (Teyssier, Pontzen & Read
2012; Penarrubia et al 2012).
In the second half of the talk, I apply the analytic techniques developed for
probing the effect of gas on dark matter dynamics to the question of how, in
the absence of baryons, a universal "NFW" dark matter halo profile
emerges (independent of scale or details of the initial conditions).
Thus the generation of NFW halos on the one hand and the destruction of their
central cusps on the other can be ascribed to surprisingly similar physical