Hydrogen introduced in compound semiconductors generally forms complexes with atoms of the crystal. They result from the interaction of hydrogen with some dopants, residual impurities and defects. It is shown here how vibrational spectroscopy can inform on the chemical nature of the complexes and on their structure, which can explain some electrical effects. From the experimental data, a kind of classification of the complexes, depending on the binding and location of the H atom, is established. Spectroscopy under uniaxial stress allows to determine the symmetry of the complexes and the relation with theoretical models is discussed. From the stress-induced dichroism one can derive reorientation energies related to the lattice distortion induced by the complex. An overview of the complexes in proton-implanted materials is presented and we finally try to summarize some of the questions not yet answered on the interaction between hydrogen and bulk compound semiconductors.