High peak current for vehicle starting, recuperation of regenerative braking energy, longer battery lifespan, and more significant acceleration among others in modern transport vehicles (TVs) require increased battery size. Moreover, batteries have high energy density and low power density. Therefore, a big battery pack can weigh more, shorten its lifespan, increase vehicle total mass, and increase battery degradation costs. On the one hand, higher power energy storage systems (ESSs) such as supercapacitors, lithium-ion capacitors, and superconducting magnetic ESSs have a lower energy density, higher power density, and greater lifespan. Thus, to satisfy the requirements of modern TVs, the combination of higher energy and higher power density can provide enhanced performance and a longer battery lifespan for these vehicles. Available research publications in the literature have addressed a similar problem. However, these publications have reported the findings separately, providing various research and conclusions.Currently, no available literature has compiled an intelligible and combined analysis for addressing hybrid ESS configurations, sizing methods, and energy management strategies to create further knowledge in this domain. There is a need to consolidate a compact and insightful knowledge toward this research direction for a more significant societal and industrial impact. This paper critically reviews the hybrid higher energy density batteries and higher power density ESSs used in TVs. It discusses the integration configurations, applications, and provides sizing methods to achieve the best hybrid energy storage systems (HESSs). Also, applied control methods are described for these HESSs such that the overall system performance matches the vehicle requirements. Lastly, it provides insights and future research direction for HESS configuration, sizing, and control.