Electrification in the transportation industry is becoming more important to face global warming and replace fossil fuels in the future. Among the available energy sources Li-ion battery and proton exchange membrane fuel cell (PEMFC) are the most promising energy sources. Therefore, employing them in fuel cell hybrid electric vehicles (FCHEVs) to combine their advantages is one of the favorable solutions. However, they still face a major challenge residing in their aging that cause the drop of system performance. On one hand, the degradation is the result of the interaction between several aging mechanisms that react differently with various operating conditions. On the other hand, a hybrid system requires an essential energy management strategy (EMS) for fuel economy and optimal power share. At the end, this EMS has an important impact on the lifetime of sources in term of reducing or favorizing the degradation. Therefore, it is important to consider the degradation in the objectives of the designed EMS. Since the degradation is usually neglected when designing an EMS, this paper tends to review the possible methods for designing a health-conscious EMS. Hence, this paper presents a summary of the main fuel cell (FC) and Li-ion battery aging mechanisms as well as the useful degradation models for state of health estimation. In addition, the existing works that consider the degradation of on-board energy sources in their approaches for increasing their durability are classified and analysed. Remaining challenges are detailed along with a discussion and outlooks about current and future trends of health-conscious EMS.