This thesis deals with the dynamical nature of the glass transition. In a first part, we study a class of mean field spin glass models. We show that the nature of the spin glass transition, either continue with full replica symetry breaking or structural with one step replica symetry breaking, can be infered directly from the density of eigenvalues of the coupling matrix, and more precisely from its behavior around its largest eigenvalue, that is to say the one with lowest energy. The dynamical transition corresponding to the appearence of a very large number of metastable states, we study their number in the generalized random orthogonal model, which is a kind of Hopfield model with extensive number of patterns but where the patterns are strictly orthogonals. We study the influence of pattern orthogonality on the number of one flip stable states. The analytical studies are complemented with numerical simulations. We carry out both the Monte Carlo simulations and exact enumerations on small systems which directly gives access to the equilibrium quantities or the number of one flip stable states with excellent agreement with analytical predictions.\ In a second part, we study a model without disorder where the order parameter possesses $O(N)$ symmetry but where the ground states are not all equivalent. This model schematically describes the relaxation towards a cristalline or amorph state of a system of hard spheres colloids. We show that the amorphe state is favoured by the dynamics and we study the attraction bassin of both phases for the zero temperature dyanamics : analytically in the large $N$ limit and numerically when $N$ is finite.
