Efficient and reliable energy storage systems are crucial for our modern society. Lithium-ion batteries (LIBs) with excellent performance are widely used in portable electronics and electric vehicles (EVs), but frequent fires and explosions limit their further and more widespread applications. This review summarizes aspects of LIB safety and discusses the related issues, strategies, and testing standards. Specifically, it begins with a brief introduction to LIB working principles and cell structures, and then provides an overview of the notorious thermal runaway, with an emphasis on the effects of mechanical, electrical, and thermal abuse. The following sections examine strategies for improving cell safety, including approaches through cell chemistry, cooling, and balancing, afterwards describing current safety standards and corresponding tests. The review concludes with insights into potential future developments and the prospects for safer LIBs.