Over the past four decades, cosmologists have assumed that dark matter
is made of cold (non-relativistic) and non-interacting hypothetical
particles with typical mass m~100GeV leading to the cold dark matter
(CDM) paradigm. Although this hypothesis describe the large-scale
distribution of galaxies in the universe, there are long-standing
discrepancies at small-scales that suggest we do not have the complete
picture,e.g. cusp-core and too-big-to-fail problems. To have the
complete picture, we need numerical simulations exploring the synergy
between baryonic matter and new dark matter physics beyond CDM. I will
discuss the implications of new cosmological simulations with
self-interacting dark matter and quantum (fuzzy) dark matter on
small-scale challenges, addressing how these simulations offer a new
path to probe the fundamental nature of dark matter.