I will review known analytic results for supersymmetric partition functions of three-dimensional CFTs that arise in M-theory. Localization techniques can be used to recast these observables in terms of matrix models, and the latter can sometimes be solved exactly using connections to statistical physics systems and/or topological string theory. Motivated by holography, I will then present a conjecture in the cases where such connections have yet to be uncovered. This, along with ongoing numerical studies, points to interesting structures awaiting to be discovered in the CFT3 matrix models.