A number of facts established in numerous experiments on the nonlinear collective interaction of a monoenergetic electron beam with plasma and never previously satisfactorily explained became understandable after the concept of dense bunches, into which an electron beam separates, was developed in the 1970s. In this review, in addition to a description of these facts, the results of theoretical investigations of the formation and evolution of bunches under the conditions of stationary beam injection into a plasma with different parameters are presented. The role of higher-order harmonics of the electric field, dissipation, and plasma temperature is discussed. Special attention is given to experiments concerned with a direct study of the dynamics of electron bunches in plasma. Possible reasons for the observed rapid breakup of these bunches are enumerated. Results of experimental and theoretical investigations of the equilibrium state of bunches, created outside the plasma and then injected into it, are also examined. Under certain conditions, such bunches are conserved in a plasma much better than bunches that form spontaneously, while the periodic quasistationary waves created by them (Bemstein-Green-Kruskal waves) propagate much farther than evolving waves, which are excited when a continuous beam is injected into a plasma.