Since its original inception, a great deal has been learned about the nature, properties, and applications of the H-bond. This review summarizes some of the unexpected paths that inquiry into this phenomenon has taken researchers. The transfer of the bridging proton from one molecule to another can occur not only in the ground electronic state, but in various excited states as well. Study of the latter process has developed insights into the relationships between the nature of the state, the strength of the H-bond, and the height of the transfer barrier. The enormous broadening of the range of atoms that can act as both proton donor and acceptor has led to the concept of the CH···O HB, whose properties are of immense importance in biomolecular structure and function. The idea that the central bridging proton can be replaced by any of various electronegative atoms has fostered the rapidly growing exploration of related noncovalent bonds that include halogen, chalcogen, pnicogen, and tetrel bonds.