In this Lecture I will discuss generic properties of superfluidity in conservative and driven-dissipative quantum many-body systems. For the last one the model ofexciton polariton condensate  in an incoherently pumped semiconductor microcavity with an embedded weak-contrast lattice and coupled to an exciton reservoir is examined in detail. Various non-trivial  nonlinear regimes and “swallow tails” catastrophes  are discussed in the framework of superfluidity manifestation at the edges of Brillouin zone.