in the past decade, superfluid ultracold gases and liquids have become the physicists' preferred domain for exploring novel phenomena in condensed matter, and for testing many-body theories of how atoms interact with each other. there is an explosion of the new quantum fluids discovered, that challenge both mathematicians and physicists by their fascinating, yet enigmatic behaviors. the most famous of them is the ability to flow through narrow gaps without any friction and energy dissipation and the existence of quantized vortices. different problems and approaches in mathematical modeling of the macroscopic superfluid dynamics will be discussed. particular emphasis will be given to the formation of coherent structures and the quantized vortex dynamics.