Anosov representations are representations of a hyperbolic group to a non-compact semisimple Lie group that are “geometrically well-behaved”. In the case when the target Lie group is PGL(d, R), these representations admit a limit set in d − 1 dimensional projective space that is homeomorphic to the boundary of the group. Under some irreducibility conditions, we give necessary and sufficient conditions for when this limit set is a C1,a sub manifold. This is joint work with A. Zimmer.