The quantum random energy model serves as a simple cornerstone, and a testing ground, for a number of fields.  It is the simplest of all mean-field spin glass models in which quantum effects due to the presence of a transversal field are studied.  Renewed interest in its spectral properties arose recently in connection with many-body localisation. In this talk I will review some of the conjectures related to this model and present a derivation of the key features of its thermal phase diagram.