The review summarizes the experimental and theoretical advances in the elucidation of the nature, the structure, the spectral and energetic characteristics of the new types of hydrogen bonds (HB) specifically for organometallic compounds: cationic hydride as a proton donor ([MH] + ...OP(X - )) and a metal atom (M...HX) or hydride ligand (MH...HX) as a proton acceptor. The main features of new unconventional and classical HB appear to be similar. The influence of different factors on HB and full proton transfer is analyzed. Investigations of HB participation in proton transfer reactions as intermediates as well as approaches to experimental energy profiles of protonation are presented.