The Brewer-Engel valence-bond theory for bonding in metals and intermetallic phases has been employed to correlate the electrocatalytic features of both individual and composite transition metal catalysts for the hydrogen evolution reaction (HER). The basic concept of the Brewer-Engel valence-bond theory, that relates the electronic state of highest multiplicity that corresponds to the electronic configuration of lowest energy level or the structure of atoms, with the corresponding phase structure in both individual metallic and multicomponent intermetallic systems, is also given. On the basis of the Brewer intermetallic bonding model as a generalized Lewis acid-base reaction, it is pointed out that, whenever metals of the left half of the transition series, having empty or half-filled vacant d-orbitals, are alloyed with metals of the right half of the transition series, having internally paired d-electrons not available for bonding in the pure metal, that proceeds with definite charge transfer, there arises a well-pronounced synergism in electrocatalysis for the HER, that often exceeds the individual catalytic effects of the precious metals by themselves or in combination (the synergism condition), and approaches reversible behavior within a wide range of current density. Brewer intermetallic phases of hypo-hyper-d-electronic transition metals have been theoretically considered and practically investigated across the corresponding phase diagrams as electrocatalysts for the HER, and their activity explained on the basis of the d-d electronic correlations. It is inferred that the maximum electrocatalytic activity extends to the composite d-metal catalysts of improved d-orbital overlap in intermetallic phases of highest symmetry and minimal enropy, such as Laves phases, and A15 or Cr3Si types, such as MoCo3, WNi3, VNi3, HfPd3, TiPt3, WFe3, ZrPt3, and LaNi5, that the Brewer theory for intermetallic bonding predicts for the most stable systems.