Spin photocurrents generated by homogeneous optical excitation with circularly polarized radiation in quantum wells (QWs) are reviewed. The absorption of circularly polarized light results in optical spin orientation due to the transfer of the angular momentum of photons to electrons of a two-dimensional electron gas. It is shown that in QWs belonging to one of the gyrotropic crystal classes a non-equilibrium spin polarization of uniformly distributed electrons causes a directed motion of electrons in the plane of the QW. A characteristic feature of this electric current, which occurs in unbiased samples, is that it reverses its direction upon changing the radiation helicity from left-handed to right-handed and vice versa. Two microscopic mechanisms are responsible for the occurrence of an electric current linked to a uniform spin polarization in a QW: the spin polarization-induced circular photogalvanic effect and the spin-galvanic effect. In both effects the current flow is driven by an asymmetric distribution of spin-polarized carriers in k-space of systems with lifted spin degeneracy due to k-linear terms in the Hamiltonian. Spin photocurrents provide methods to investigate spin relaxation and to reach a conclusion as regards the in-plane symmetry of QWs. The effect can also be utilized to develop fast detectors for determining the degree of circular polarization of a radiation beam. Furthermore, spin photocurrents under infrared excitation were used to demonstrate and investigate monopolar spin orientation of free carriers.