A reciprocating engine without a crank-slider mechanism is called a free-piston engine. If the piston is directly connected to a linear alternator, it is called a free-piston linear alternator. Free-piston engines and free-piston linear alternators have the potential to offer solutions for future hybrid electric vehicles and stationary power generation, by enabling direct conversion of mechanical energy to electricity. They benefit from reduced friction losses compared to conventional engines and can have variable compression ratio, which enables combustion control and optimization. Their widespread application has been limited by the necessity for high-speed control strategies. However, their operating characteristics can provide high efficiency, especially when used with low temperature combustion strategies. Low temperature combustion combines the high thermal efficiency of diesel engines, with the low soot emissions of spark-ignition engines, and low NO x emissions because of low burned gas temperatures. This article provides a comprehensive review of free-piston engine technology, with a focus on advanced combustion processes and their potential for use in future powertrain systems.