We overview the recent experimental and theoretical works on spin-transport in semiconductor structures related to the spin Hall effect (SHE). After its first prediction in 1971 by M.I. Dyakonov and V.I. Perel' this effect has been quite rarely mentioned in literature during almost 30 years, while at the beginning of the new millennium a worldwide wave of interest to it emerged, and many related effects have been proposed. Here we discuss 'extrinsic' and 'intrinsic' SHEs for carriers and the optical SHE for exciton-polaritons.