The dissertation delas with existence and nonexistence results for a class of nonlinear elliptic systems which arise in looking for solitary waves in coupling the matter field with the electromagnetic field when the nonlinearity exhibits some critical behaviour; in particular this is the case of solitons which are in equilibrium with their own electromagnetic field. In the second part of the dissertation, the author develop a technique to characterize, in a variational framework, the ground state energy level of a large class of critical Hamiltonian elliptic systems.