To advance current Li rechargeable batteries further, tremendous emphasis has been made on the development of anode materials with higher capacities than the widely commercialized graphite. Some of these anode materials exhibit capacities above the theoretical value predicted based on conventional mechanisms of Li storage, namely insertion, alloying, and conversion. In addition, in contrast to conventional observations of loss upon cycling, the capacity has been found to increase during repeated cycling in a significant number of cases. As the internal environment in the battery is very complicated and continuously changing, these abnormal charge storage behaviors are caused by diverse reactions. In this review, we will introduce our current understanding of reported reactions accounting for the extra capacity. It includes formation/decomposition of electrolyte-derived surface layer, the possibility of additional charge storage at sharp interfaces between electronic and ionic sinks, redox reactions of Li-containing species, unconventional activity of structural defects, and metallic-cluster like Li storage. We will also discuss how the changes in the anode can induce capacity increase upon cycling. With this knowledge, new insights into possible strategies to effectively and sustainably utilize these abnormal charge storage mechanisms to produce vertical leaps in performance of anode materials will be laid out.