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Stirling engines are one of the possible technological solutions enabling the management of renewable and waste energy sources. Currently, their main commercial application, however, is the production of heat and electricity from conventional energy sources, such as natural gas, diesel oil. One of the most important technical problems related to the use of Stirling engines to generate electricity from low-temperature energy sources is the need to meet two basic countercurrent requirements, minimizing the dead volume associated with transporting the working gas between the compression and expansion spaces, and maximizing the heat exchange surface to provide the right amount of heat to the system with a low-temperature difference. The optimization of the Stirling engine design requires very precise mapping of the influence of the above-mentioned design features on the efficiency and power of the system. For this purpose, computational models with varying degrees of details and accuracy are used. The paper presents an overview of the technology development of modern Stirling engines and the computational models used for the development of these structures.