The complexity of contemporary energy arrangements created the necessity to apply not only a process approach, but also a system approach in energy and exergy analyses. This distinction was developed at Professor Jan Szargut's Silesian School of Thermal Engineering in the 1960s, and Input-output (1-0) analysis as a method of mathematical modelling of energy systems was applied. The 1-0 linear mathematical model of the energy economy of an industrial plant was then developed, and the following problems were resolved: - optimisation of the mathematical model in order to select the optimal structure of the energy economy of industrial plants within the framework of preliminary design, - nonlinear mathematical model of the energy management of ironworks for control and scheduling, - system analysis of the exergy losses considering the energy systems of ironworks, - mathematical model of the energy production system of complex buildings, and - application of the 1-0 model in energy and exergy analyses of oxy-fuel combustion power plants with CO2 capture, transport, and storage. The 1-0 method was also applied in the modelling of calculations of the cumulative energy and exergy consumption, cumulative emissions, and the indices of thermo-ecological costs. (C) 2018 Elsevier Ltd. All rights reserved.