The Stirling engine is an alternative solution to produce cleaner energy in order to achieve the reduction of the fossil fuel consumption and the CO2 emissions. It comprises an external combustion engine that can convert any external heat source into mechanical power, through cyclic expansion and compression of a working gas in a closed-regenerative cycle, with or without driving mechanisms. The free-piston Stirling Engine is significantly preferred because of the absence of any mechanical linkage resulting in longer operating life, lower noise pollution, maintenance and vibration free, self-starting and high thermal efficiency. The aim of this paper is to summarize the research works on the free-piston Stirling engine technologies and models. First, the working principles of the free-piston Stirling engine are described, identifying different configurations. Then, several applications are presented. Finally, a detailed review of the models available in literature is given, pointing out the main assumptions and equations.