This study provides an overview of available techniques for on-board State-of-Available-Power (SoAP) prediction of lithium-ion batteries (LIBs) in electric vehicles. Different approaches dealing with the on-board estimation of battery State-of-Charge (SoC) or State-of-Health (SoH) have been extensively discussed in various researches in the past. However, the topic of SoAP prediction has not been explored comprehensively yet. The prediction of the maximum power that can be applied to the battery by discharging or charging it during acceleration, regenerative braking and gradient climbing is definitely one of the most challenging tasks of battery management systems. In large lithium-ion battery packs because of many factors, such as temperature distribution, cell-to-cell deviations regarding the actual battery impedance or capacity either in initial or aged state, the use of efficient and reliable methods for battery state estimation is required. The available battery power is limited by the safe operating area (SOA), where SOA is defined by battery temperature, current, voltage and SoC. Accurate SoAP prediction allows the energy management system to regulate the power flow of the vehicle more precisely and optimize battery performance and improve its lifetime accordingly. To this end, scientific and technical literature sources are studied and available approaches are reviewed.