The partition function and expectation values of certain BPS observables of N>=2 Chern-Simons-matter theories on the three-sphere are known to reduce to a finite dimensional matrix integral. We analyze these matrix models by different methods. We find different properties and exact results and provide various explicit and non-trivial checks of the AdS_4/CFT_3 conjecture. In particular we find the N^{3/2} behavior in the strong coupling limit predicted from string theory. In the case of ABJM theory we find a relation to topological strings on local P^1xP^1. We also find a connection between the strong coupling limit and the tropical limit for the spectral curve. We show that for theories with at least N=3 supersymmetry the partition function can be interpreted as a partition function of a certain free Fermi gas which allows us to find an explicit and exact answer for the perturbative part of the partition function.