Unlike normal chemical bonds, hydrogen bonds (H-bonds) characteristically feature binding energies and contact distances that do not simply depend on the donor (D) and acceptor (:A) nature. Instead, their chemical context can lead to large variations even for a same donor-acceptor couple. As a striking example, the weak HO-H...OH(2) bond in neutral water changes, in acidic or basic medium, to the 6-fold stronger and 15% shorter [H(2)O...H...OH(2)](+) or [HO...H...OH](-) bonds. This surprising behavior, sometimes called the H-bond puzzle, practically prevents prediction of H-bond strengths from the properties of the interacting molecules. Explaining this puzzle has been the main research interest of our laboratory in the last 20 years. Our first contribution was the proposal of RAHB (resonance-assisted H-bond), a new type of strong H-bond where donor and acceptor are linked by a short pi-conjugated fragment. The RAHB discovery prompted new studies on strong H-bonds, finally leading to a general H-bond classification in six classes, called the six chemical leitmotifs, four of which include all known types of strong bonds. These studies attested to the covalent nature of the strong H-bond showing, by a formal valence-bond treatment, that weak H-bonds are basically electrostatic while stronger ones are mixtures of electrostatic and covalent contributions. The covalent component gradually increases as the difference of donor-acceptor proton affinities, DeltaPA, or acidic constants, DeltapK(a), approaches zero. At this limit, the strong and symmetrical D...H...A bonds formed can be viewed as true three-center-four-electron covalent bonds. These results emphasize the role PA/pK(a) equalization plays in strengthening the H-bond, a hypothesis often invoked in the past but never fully verified. In this Account, this hypothesis is reconsidered by using a new instrument, the pK(a) slide rule, a bar chart that reports in separate scales the pK(a)'s of the D-H proton donors and :A proton acceptors most frequently involved in D-H...:A bond formation. Allowing the two scales to shift so to bring selected donor and acceptor molecules into coincidence, the ruler permits graphical evaluation of DeltapK(a) and then empirical appreciation of the D-H...:A bond strength according to the pK(a) equalization principle. Reliability of pK(a) slide rule predictions has been verified by extensive comparison with two classical sources of H-bond strengths: (i) the gas-phase dissociation enthalpies of charged [X...H...X](-) and [X...H...X](+) bonds derived from the thermodynamic NIST Database and (ii) the geometries of more than 9500 H-bonds retrieved from the Cambridge Structural Database. The results attest that the pK(a) slide rule provides a reliable solution for the long-standing problem of H-bond-strength prediction and represents an efficient and practical tool for making such predictions directly accessible to all scientists.