All cases of strong (2.50 less than or equal to d(O-O) < 2.65 Angstrom) and very strong (d(O-O) < 2.50 Angstrom) O-H-O hydrogen bonds whose, geometries are known from accurate neutron or X-ray diffraction studies are reviewed and classified in chemical classes belonging to three fundamental types : (A) -O-H-O-, or negative charge assisted hydrogen bonding, (-)CAHB; (B) =O-H+-O=, or positive charge assisted hydrogen bonding, (+)CAHB; and (C) -O-H-O=, where the two oxygens are interconnected by a system of pi-conjugated double bonds, or resonance-assisted hydrogen bonding, RAHB. An empirical model is discussed where the hydrogen bond energy is expressed as E(HB)= E(COV) + E(EL) + E(REP), E(COV) being the energy of the covalent three-center-four-electron 0.-.H-:O bond, and E(EL) and E(REP), the electrostatic attraction and interoxygen repulsion energies, respectively. By means of a detailed analysis of bond and contact distances, it is shown that, while the O-O distance is shortened from 2.80 to 2.40 Angstrom, the hydrogen bond is transformed from a dissymmetrical O-H-O electrostatic interaction to a covalent and symmetrical O-H-O bond. It is suggested that such behavior is common to all homonuclear hydrogen bonds (O-H-O, N-H-N, F-H-F), while heteronuclear ones (e.g. N-H-O) can only give weaker bonds of mostly:electrostatic nature.