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Loop quantum gravity has provided us with a canonical framework especiallydevised for background independent and diffeomorphism invariant gauge fieldtheories. In this quantization the fundamental excitations are called spinnetwork states, and in the context of general relativity, they give a meaningto quantum geometry. Spin foams are a sort of path integral for spin networkstates, supposed to enable the computations of transition amplitudes betweenthese states. The spin foam quantization has proved very efficient fortopological field theories, like 2d Yang-Mills, 3d gravity or BF theories.Different models have also been proposed for 4-dimensional quantum gravity. Inthis PhD manuscript, I discuss several methods to study spin foam models. Inparticular, I present some recurrence relations on spin foam amplitudes, whichgenerically encode classical symmetries at the quantum level, and are likely tohelp fill the gap with the Hamiltonian constraints. These relations can benaturally interpreted in terms of elementary deformations of discrete geometricstructures, like simplicial geometries. Another interesting method consists inexploring the way spin foam models can be written as path integrals for systemsof geometries on a lattice, taking inspiration from topological models andRegge calculus. This leads to a very geometric view on spin foams, and givesclassical action principles which are studied in details.

G\'eom\'etrie quantique dans les mousses de spins : de la th\'eorie topologique BF vers la relativit\'e g\'en\'erale