The successes of the Weinberg-Salam model and quantum chromodynamics have made the attempt at the unification of weak, electromagnetic, and strong interactions of leptons and quarks in the framework of a single group into a serious proposition. The simplest and most economic unifying group is SU(5). The review is devoted to a detailed study of some of the questions associated with the unification of the interactions of the elementary particles in the example of the group SU(5). The questions considered include the part played by ``natural'' conservation of the quark flavor by neutral weak currents in searches for unifying groups, the ``quantization'' of charge (connection between the charges of quarks and leptons), the renormalization of unified groups to present-day energies, the instability of the nucleon, the finiteness of the number of flavors, the hierarchy of interactions unified in a single scheme, and the cosmological aspects of unification schemes. Other ``grand unification'' schemes are also considered briefly. Some possible ways of constructing unifying schemes are discussed in the conclusions.