High-energy rechargeable lithium (Li) metal batteries (LMBs) with Li metal anode (LMA) were first developed in the 1970s, but their practical applications have been hindered by the safety and low-efficiency concerns related to LMA. Recently, a worldwide effort on LMA-based rechargeable LMBs has been revived to replace graphite-based, Li-ion batteries because of the much higher energy density that can be achieved with LMBs. This review focuses on the recent progress on the stabilization of LMA with nonaqueous electrolytes and reveals the fundamental mechanisms behind this improved stability. Various strategies that can enhance the stability of LMA in practical conditions and perspectives on the future development of LMA are also discussed. These strategies include the use of novel electrolytes such as superconcentrated electrolytes, localized high-concentration electrolytes, and highly fluorinated electrolytes, surface coatings that can form a solid electrolyte interphase with a high interfacial energy and self-healing capabilities, development of "anode-free" Li batteries to minimize the interaction between LMA and electrolyte, approaches to enable operation of LMA in practical conditions, etc. Combination of these strategies ultimately will lead us closer to the large-scale application of LMBs which often is called the "Holy Grail" of energy storage systems.