  We study large deviation properties of systems of weakly interacting
particles modeled by It\^{o} stochastic differential equations (SDEs). It is
known under certain conditions that the corresponding sequence of empirical
measures converges, as the number of particles tends to infinity, to the weak
solution of an associated McKean-Vlasov equation. We derive a large deviation
principle via the weak convergence approach. The proof, which avoids
discretization arguments, is based on a representation theorem, weak
convergence and ideas from stochastic optimal control. The method works under
rather mild assumptions and also for models described by SDEs not of diffusion
type. To illustrate this, we treat the case of SDEs with delay.
