With the trend of low emissions and sustainable development, the demand for hybrid electric vehicles (HEVs) has increased rapidly. By combining a conventional internal combustion engine with one or more electric motors powered by a battery, HEVs have the advantages over traditional vehicles in better fuel economy and lower tailpipe emissions. Nevertheless, the power management strategies (PMSs) for conventional vehicles which mainly focus on the efficiency of internal combustion engine are no longer applicable due to the complex internal structure of HEVs. Hence, a large number of novel strategies appropriate for HEVs have been surveyed, but most of the researches concentrate on discussing the classifications of PMSs and comparing their cons and pros. This paper presents a comprehensive review of power management strategies adopted in HEVs aiming at specific challenges for the first time. The categories of the existing PMSs are presented based on the different algorithms, followed by a brief study of each type including the analysis of its pros and cons. Afterwards, the implementation and optimization of power management strategies aiming at proposed challenges are introduced in detail with the description of their optimization objectives and optimized results. Finally, future directions and open issues of PMSs in HEVs are discussed.