A peculiar situation which has persisted for a quarter of a century in the theory of the multiple production of high-energy hadrons is reviewed. On the one hand, cosmic-ray work established the concept of heavy intermediate formation--fireballs--a long time ago. The evolution and decay of these fireballs can be described thermodynamically (in particular, hydrodynamically). On the other hand, the advent of ultrarelativistic proton accelerators stimulated Feynman-diagram, peripheral, and Regge approaches to the description of few-particle events; later, multiperipheral, parton (``parton comb''), etc., approaches were taken to describe many-particle events. Over the past decade, the failure of Feynman scaling in the pionization region, the observation of clustering, etc., and the success of the thermodynamic interpretation of accelerator experiments, which has won new support from quantum chromodynamics, have marked a substantial convergence of the models which previously appeared mutually exclusive. A suitable approximate model describing this convergence is a model which has been under development for a long time now, peripheral or even multiperipheral in its essence but including thermodynamic subsystems. This convergence now seems even more pronounced than was thought only recently; the characteristics of thermodynamic entities are manifested time and time again in accelerator experiments. At the same time, for processes involving only a few particles (which thermodynamics cannot claim to describe), the picture is still dominated by both the phenomenological interpretation, based on reggeon exchange, and the quantum chromodynamics of point quarks for deep inelastic reactions involving the transfer of a large 4-momentum (the same is true for reactions involving the fragmentation of the incident particle or of the target).