The ultrafast dynamics of optical excitations in semiconductors and semiconductor nanostructures can be computed on a microscopic theoretical basis using the semiconductor Bloch equations. This set of equations allows one to nonperturbatively evaluate light-field-induced intraband and interband excitations and is also well suited for the analysis of many-body effects such as excitonic resonances and carrier-carrier and carrier-phonon scattering processes. In this article we start with a description of an experimental observation of coherent spin photocurrents, then we briefly introduce the theoretical approach and review some results of our theory concerning the microscopic description of the ultrafast coherent optical generation and the temporal decay of charge and spin currents in semiconductor nanostructures. The computed transients show an enhanced damping of the spin current relative to the charge current as a consequence of Coulomb scattering between carriers with opposite spin. The influence of quantum kinetic memory effects on the dynamics of the photocurrents is analyzed by evaluating the scattering terms beyond the Markov approximation.