We study various aspects of the matrix models calculating free energies and
Wilson loop observables in supersymmetric Chern-Simons-matter theories on the
three-sphere. We first develop techniques to extract strong coupling results
directly from the spectral curve describing the large N master field. We show
that the strong coupling limit of the gauge theory corresponds to the so-called
tropical limit of the spectral curve. In this limit, the curve degenerates to a
planar graph, and matrix model calculations reduce to elementary line integrals
along the graph. As an important physical application of these tropical
techniques, we study N=3 theories with fundamental matter, both in the quenched
and in the unquenched regimes. We calculate the exact spectral curve in the
Veneziano limit, and we evaluate the planar free energy and Wilson loop
observables at strong coupling by using tropical geometry. The results are in
agreement with the predictions of the AdS duals involving tri-Sasakian
manifoldsComment: 32 pages, 7 figures. v2: small corrections, added an Appendix on the
relation with the approach of 1011.5487. v3: further corrections and
clarifications, final version to appear in JHE
