This review summarizes the presently available knowledge concerning hydrogen-impurity complexes in III-V compounds. The impurities form shallow acceptors on group III sites (Be, Zn, Cd) and on group V sites (C, Si, Ge) as well as shallow donors on group V sites (S, Se, Te) and on group III sites (Si, Sn). These complexes are mainly revealed by their hydrogen stretching modes. Therefore, nearly all information about their structure and dynamic properties is derived from vibrational spectroscopy. The complexes of shallow impurities with hydrogen have been most extensively investigated in GaAs, GaP and InP. This holds also for Mg-H in GaN. The complexes exhibit a different microscopic structure, which is discussed in detail. The isoelectronic impurity nitrogen, complexed with one hydrogen atom, is investigated in detail in GaAs and GaP. Those complexes can exist in different charge states. The experimental results such as vibrational frequencies, the microscopic structure and the activation energy for reorientation for many of these complexes are in very good agreement with results of ab initio calculations. Different types of oxygen-hydrogen complexes in GaAs and GaP are described, with one hydrogen atom or two hydrogen atoms bonded to oxygen. Three of these complexes in GaAs were found to be electrically active.