i will discuss recent joint results with b. lamel addressing the $c^\infty$ regularity problem for cr mappings between smooth cr submanifolds in complex spaces of possibly different dimension. we essentially show that a nowhere smooth cr map must have its image contained in the set of d’angelo infinite type points of the target manifold, from which we derive a number of new regularity results, even in the hypersurface case. applications to the boundary regularity of proper holomorphic mappings will also be mentioned.