  We introduce the time-dependent restricted active space Configuration
Interaction method to solve the time-dependent Schr\"odinger equation for
many-electron atoms, and particularly apply it to the treatment of
photoionization processes in atoms. The method is presented in a very general
formulation and incorporates a wide range of commonly used approximation
schemes, like the single-active electron approximation, time-dependent
Configuration Interaction with single-excitations, or the time-dependent
R-matrix method. We proof the applicability of the method by calculating the
photoionization cross sections of Helium and Beryllium, as well as the
X-ray--IR pump-probe ionization in Beryllium
