Abstract
A brief review of the development of ideas on extremal principles in the theory of heat and mass transfer processes (including those in reacting media) is given. The extremal principles of non-equilibrium thermodynamics are critically examined. Examples are shown in which the mechanical use of entropy production-based principles turns out to be inefficient and even contradictory. The main problem of extremal principles in the theory of irreversible processes is the impossibility of their generalization, often even within the framework of a class of problems. Alternative extremal formulations are considered: variational principles for heat and mass transfer equations and other dissipative systems. Several extremal principles are singled out, which make it possible to simplify the numerical solution of the initial equations. Criteria are proposed that allow one to classify extremal principles according to their areas of applicability. Possible directions for further research in the search for extremal principles in the theory of irreversible processes are given.