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Batteries are presently pervasive in portable electronics, electrified vehicles, and renewable energy storage. These indispensable engineering applications are all safety-critical and energy efficiency-demanding such that batteries must be meticulously monitored and manipulated, where effectively estimating the internal battery states is a key enabler. The primary goal of this paper is to present a concise, understandable overview of existing methods, key issues, technical challenges, and future trends of the battery state estimation domain. More specifically, for the first time, the state of the art in State of Charge (SOC), State of Energy (SOE), State of Health (SOH), State of Power (SOP), State of Temperature (SOT), and State of Safety (SOS) estimation is all elucidated in a tutorial yet systematical way, along with existing issues exposed. In addition, from six different viewpoints, some future important research opportunities and evolving trends of this prosperous field are disclosed, in order to stimulate more technologically innovative breakthroughs in SOC/SOE/SOH/SOP/SOT/SOS estimation. • Critical battery internal states are defined and explained. • Battery state estimation methods are systematically overviewed. • Key issues, technical challenges and opportunities are elucidated. • Future research directions and trends are presented. [ABSTRACT FROM AUTHOR]