Lithium ion batteries (LIBs) are the state-of-the-art technology among electrochemical energy storage and conversion cells, and are still considered the most attractive class of battery in the future due to their high specific energy density, high efficiency, and long cycle life. Rapid development of power-hungry commercial electronics and large-scale energy storage applications (e.g. off-peak electrical energy storage), however, requires novel anode materials that have higher energy densities to replace conventional graphite electrodes. Germanium (Ge) and silicon (Si) are thought to be ideal prospect candidates for next generation LIB anodes due to their extremely high theoretical energy capacities. For instance, Ge offers relatively lower volume change during cycling, better Li insertion/extraction kinetics, and higher electronic conductivity than Si. In this focused review, we briefly describe the basic concepts of LIBs and then look at the characteristics of ideal anode materials that can provide greatly improved electrochemical performance, including high capacity, better cycling behavior, and rate capability. We then discuss how, in the future, Ge anode materials (Ge and Ge oxides, Ge-carbon composites, and other Ge-based composites) could increase the capacity of today's Li batteries. In recent years, considerable efforts have been made to fulfill the requirements of excellent anode materials, especially using these materials at the nanoscale. This article shall serve as a handy reference, as well as starting point, for future research related to high capacity LIB anodes, especially based on semiconductor Ge and Si.