In recent years, a significant interest in hybrid and battery electric vehicles has arisen globally due to reducing fuel consumption, mitigating dependence on imported oil and decreasing greenhouse gas emissions. The overall success of these vehicles mostly depends on the performance of sub-systems that they are created. In order to enhance the performances of these sub-systems, estimation of their parameters with high accuracy is required. Furthermore, estimation strategies play an important role in battery management, vehicle energy management and vehicle control by undertaking different tasks. There have been a limited number of review studies related with estimation strategies that are only focused on battery state of charge (SOC) and state of health (SOH) estimation. This paper presents a comprehensive review on various estimation strategies used in hybrid and battery electric vehicles for the first time in the literature. The existing estimation strategies are classified and different methodologies used in each estimation strategy are elaborated. Recent research advances on existing estimation strategies are clearly emphasized by reviewing numerous studies over 200 papers.