Vehicle electrification has to be addressed to reduce dependence on fossil fuels and meet future emission regulations. Pure electric vehicles still have many limitations, but hybrid vehicles are the optimum transference scheme. An over-expansion cycle (Atkinson or Miller) engine is the most suitable for hybrid vehicles. Compared with a conventional Otto cycle engine, an over-expansion cycle engine can realize a larger expansion ratio and thus, a higher therMal efficiency while maintaining a normal effective compression ratio to avoid the knock. Basics for the Atkinson and Miller cycles are introduced first. An in-depth survey on mechanical realizations for the over-expansion cycle is conducted. Challenges and general recommendations for real applications of these mechanical realizations are presented. After a comprehensive review of the advantages and applications of the "Atkinson cycle effect" in load control, reducing NOx formation and suppressing the knock, primary problems are discussed and some novel strategies are provided. Prospective technical solutions that handle the reduced effective compression ratio and power density for over-expansion cycle engines are studied and discussed. Finally, in the potential application fields of range-extended electric vehicles and cogeneration plants, a significant problem is presented; the efficiency optimum working points for the engine and generator do not match. A multi-disciplinary design and optimization methodology is provided to resolve the problem. The main objective of this paper is to explore the critical problems, challenges and prospective solutions that push forward broader applications for over-expansion cycle engines. This paper can be used as a critical review of the current state-of-the-art research for over-expansion cycle engines and also as guidance towards future research directions in this domain. (C) 2016 Elsevier Ltd. All rights reserved.