Lithium-ion batteries have emerged as a promising choice for electric vehicle applications. However, thermal runaway and related catastrophic issues perplex the research community when batteries are subjected to varying charging/discharging and different ambient temperatures. In order to keep the batteries under a safe zone of temperature, battery thermal management occupies utmost importance and hence researchers are switching over to a combination of either two or three strategies since single stragaty could not meet effective thermal management. In a combined strategy, the use of phase change materials and is highly essential due to their inherent thermo-physical properties; both organic and inorganic types have been explored. To enhance the heat dissipation, the phase change materials, regarded as composite phase materials, are being added with graphite powder, nanomaterials, metal foams, and fins are being arranged to the battery cells. The present review enumerates the recent progress made in achieving good thermal performance with hybrid/integrated battery thermal systems with an emphasis on the use of composite phase change materials. The review revealed that the hybrid strategy is performing well, machine learning and advanced optimization methods are being applied to understand the state of health of batteries. Few works are focussed on the mitigation of thermal runaway propagation serving the composite phase change materials as effective flame retardants. The current status and challenges being faced in the use of LIBs is also briefed. It is essential to develop economical integrated battery thermal management systems with parasitic power losses that are compact and safe to attract many city dwellers to adopt pure electric vehicles besides meeting the mandate of sustainable development goals. The review is an attempt to provide a ready reckoner in the area of integrated battery thermal management involving composite phase materials.