The experimental and theoretical research on the physical properties of superconducting compounds based on transition elements are reviewed. The discussed classes of compounds are those having the highest superconducting transition temperature $T_c$, frequently reaching 15$^\circ$K and higher. Two types of such compounds are considered in detail: intermetallic and covalent-ionic. The first type includes compounds with the structures of $\beta$-tungsten, CsCl, $\alpha$-Mn, $\sigma$-phase, and Laves phase. The second type includes numerous compounds with NaCl structure (carbides, nitrides, etc.) and chalcogenides. The superconducting, electronic, and lattice properties of each class of compounds are reviewed, and models of their electronic structures or calculations of their electronic spectra are presented. Not only compounds of stoichiometric composition, but also their alloys are considered. The extensive empirical material on the influence of alloying and of the composition on $T_c$ is systematized. The same properties are compared in various classes of compounds, and this makes it possible to establish a number of correlations between $T_c$ and the lattice symmetry, the electron density (the Matthias rule), and the anomalies of the lattice properties. A particularly substantial role is found to be played by the correlations with the lattice properties, namely, the largest $T_c$ of the various compounds of a given class are possessed as a rule by those representatives which exhibit some lattice instability. The review analyzes the lattice instability types that can appear in the compounds. The authors attempt to base the observed correlation on the existing theory of superconductors with tight binding. The last chapter of the review is devoted to a theoretical investigation of lattice phase transitions (observed in superconducting compounds with structures A-15, C-15, and B-2) as one of the forms of the lattice instability. A symmetry analysis is given for transitions that proceed in accord with an irreducible representation of the point $\Gamma$ of the $O_h$ group. The electronic mechanism of the lattice instability of the compounds A-15 and C-25 is described on the basis of the model of L. G. Gor'kov. This review is a continuation of the one which appears in Usp. Fiz. Nauk $\mathbf{113}$, 193, (1974) [Sov. Phys. Usp. $\mathbf{17}$, 356, (1974)] dealing with the superconducting compounds having a $\beta$-tungsten structure.