BSM (or Beyond the Standard Model) problems are the set of problems that do not find their resolution in the framework of the Standard Model of the elementary particle physics. Among these problems one the phenomenon of neutrino oscillations, the nature of dark matter and dark energy; the particle(s) resposible for inflation; the mechanism of generation of generation of the baryon asymmetry of the Universe.
It is customary to add to this list a number of fine-tunning problems, most notable gauge hierarchy problem (but also CP problem, cosmological constant problem)