Abstract: In the 70s, Alexander discovered an interesting rigidity phenomenon for holomorphic mappings sending a piece of the unit sphere in mathbb Cⁿ⁺¹ , n ≥ 1, into itself: Such a map is either constant or extends as a linear fractional mapping sending the ball into itself. This was later generalized, by numerous mathematicians, to mappings sending the sphere in \mathbb Cⁿ⁺¹ into that in \mathbb C^N+1 provided that N-n < n , and the latter codimensional estimate is sharp. It was recently discovered by Baouendi and Huang that, surprisingly, for mappings between pseudo-concave hyperquadrics, this rigidity phenomenon holds without any restriction on the codimension N-n. We will discuss some generalizations of these type of results to the case where the source manifold is not necessarily a quadric.