The classical literature in P.D.E. considers mainly boundary value problems with bounded domains, for which the solution is bounded. Stochastic control has introduced a class of stochastic differential equations (backward) with substantial connections to parabolic P.D.E. They are most often in the whole space. This raises difficulties when the solution to be considered is not bounded. In this talk we introduce B.S.D.E. (backward stochastic differential equations) and review the results which can be obtained. Considerable work is needed to handle systems of parabolic equations, which come quite naturally in the study of BSDE.