Strong hydrogen bonds are analyzed and their specific characteristics are given. These interactions are compared with typical H-bonds. All analyses included are mainly based on ab initio and DFT calculations but experimental examples of hydrogen bonds are also included, particularly those taken from crystal structure determinations. Theoretical techniques usually used to investigate inter- and intramolecular interactions are characterized, among them the decomposition scheme of the interaction energy and the Bader theory (‘atoms in molecules’—AIM). The covalent nature of very strong hydrogen bonds is also discussed. Different kinds of strong hydrogen bonds are described, including resonance assisted hydrogen bonds, charge assisted hydrogen bonds, and dihydrogen bonds. The phenomena of LBHB (low barrier hydrogen bond) and SSHB (short strong hydrogen bond) are also explained.