Finite jet determination for CR mappings

A CR mapping is a diffeomorphism between two real manifolds in complex space that satisfies tangential Cauchy-Riemann equations. We are concerned with the problem whether a CR mapping is uniquely determined by its finite jet at a point. This problem has been popular since 1970-s and the number of publications on the matter is enormous. Nevertheles, natural fundamental questions have been open. I will present a solution to a version of the problem and discuss old and recent results.