A projected dynamical system (PDS) is defined by an ODE with a nonlinear and discontinuous righthand side whose solutions are constrained to evolve only within a closed and convex subset K of a Hilbert space X. A PDS was first introduced in 1992, however references to the ODE defining it go back to the 70's. It is worth mentioning that it was first formulated in the context of applied economic problems. In this talk, we present a brief overview of this kind of systems, the mathematical questions that were studied so far in its case and some recent developments on the topic.