Linear engines, or widely called free piston engines, have their advantages compared to conventional engines with crankshafts, for example, lower friction loss, compact structure, fuel adaptability, flexible compression ratio, etc. Among the linear engine conceptual designs and prototypes, Linear Engine Generator (LEG) incorporating a linear engine (internal or external combustion) and a linear alternator provides an alternative and attractive solution for hybrid electrical powertrains in transport applications. Due to the advantages of linear engines, hydrogen, synthetic hydrogen carrier fuels and biofuels are easier to adopt on LEG, making it an appealing technology for decarbonisation. This paper explicitly reviews LEG research and development on state-of-art solutions and recent progress in linear engine improvement, linear alternator design optimisation, and integrated LEG system control. Key performance indicators of the linear engine generator, like power output, thermal and electrical efficiency, etc., are summarised to present a general picture of up-to-date LEG development. Recommendations for further LEG development are provided at the end of the paper regarding the review outcomes.