We define and analyze thermodynamic limits for various traditional and work-assisted processes of sequential development with finite rates important in engineering and biology. The thermodynamic limits are expressed in terms of classical exergy change and a residual inevitable minimum of dissipated exergy, or some extension including time penalty. We consider processes with heat and mass transfer that occur in a finite time and in equipment of finite dimension. These processes include heat and separation operations and are found in heat and mass exchangers, thermal networks, energy convertors, energy recovery units, storage systems, chemical reactors, and chemical plants. Our analysis is based on the condition that in order to make the results of thermodynamic analyses usable in engineering it is a thermodynamic limit (e.g. a lower bound for consumption or work or heat or an upper bound for work or heat production) which must be ensured for prescribed process requirements. The goal of this paper is not only to review and classify all main methods and results obtained in the field but also to consider common objections caused by misunderstanding of these methods and results. In fact, the paper contains a critical comparison of various methods applied in the field of energy generation, such as second law analyses, entropy generation minimization, approaches coming from ecology, and finite-time thermodynamics. A creative part of this paper outlines a general approach to the construction of ‘Carnot variables’ as suitable controls. Finite-rate models include minimal irreducible losses caused by thermal resistances to the classical exergy potential. Functions of extremum work, which incorporate residual minimum entropy production, are formulated in terms of initial and final states, total duration and (in discrete processes) number of stages.