The study of unitary representations of Lie groups is a classical subject in Representation theory going back to Gelfand and Harish-Chandra. The main, currently open, problem is to classify the irreducible unitary representations of semisimple Lie groups. Thanks to the work of Kirillov and Kostant the question of classifying the irreducibles fits into Geometric quantization that seeks to produce quantum mechanical systems from classical ones. In my talk I will explain some recent advances in Algebraic (a.k.a. Deformation) quantization of singular symplectic varieties and how they help to  understand unipotent representations, an important class of unitary representations that are expected to serve as building  blocks. This is based on my solo works as well as joint papers with Dmytro Matvieievskyi, Lucas Mason-Brown and Shilin Yu.