I will discuss our present understanding of the physics of the many-body localized (MBL) phase and of the novel quantum phase transition between many-body localization and quantum thermalization. The many-body localized phase can be understood as a "new" type of integrable system, where the emergent conserved quantities are localized operators (H., Nandkishore, Oganesyan, PRB 2014). The low frequency dynamics in this phase differs in important ways from that of noninteracting Anderson localization, due to "many-body resonances" (Gopalakrishnan, et al., arXiv:1502.07712). However, a thorough understanding of the MBL phase embodied in a working algorithm to systematically explore these properties remains elusive, in spite of significant efforts. Many questions about the nature of the MBL-to-thermal phase transition remain open.