The aim of this project is to investigate dynamical systems of deterministic and stochastic type, for which their state is constrained to remain in a given set of restrictions. Principally motivated by natural sciences, as well as financial mathematics, this subject places itself at the crossroad of several fields as stochastic analysis, control theory, PDE or convex analysis. Naturally arising in physical applications, the reflection of the dynamics at the boundary of the restriction domain is one of the possibilities to obtain state restrictions. Mathematical modelling of this phenomenon often uses variational inequalities, which will constitute the frame of our research. Another research topic consists in controlling the dynamics of stochastic system in order to minimize some cost functional. Therefore, our aim is to find sufficient and necessary conditions for the existence of an optimal control. This project will lead to new results on some problems such as a existence theory for (backward) stochastic variational inequalities(SVI), with normal and oblique reflection; numerical methods and optimization related to SVI; necessary and sufficient conditions for the optimality of controlled SVI; connection with state constraints PDE. We have designed this project on differential equations with state restrictions since this field enjoys great interest in contemporary mathematical research.