We will discuss the regularity of viscosity solutions for fully nonlinear Hessian equations with coefficients in some Muckenhoupt class. We prove Holder and higher regularity under mild assumptions on the coefficients. In particular, surprisingly, we achieve Holder differentiability across the submanifold where the ellipticity vanishes. This is a consequence of the uniqueness of suitably defined viscosity solutions. We use approximation techniques in the spirit of Caffarelli's seminal approach. This is a joint work with Yannick Sire from JHU.