The review describes the history of the creation of chemical power sources with anodes based on lithium or its alloys with aprotic (non-aqueous) and molten electrolytes, thermoelectrochemical cells, thermal chemical power sources, chemical power sources with reactive emerging electrolyte. Creating a lithium-ion battery (LIB) is connected with the use of graphite as a matrix for lithium. Graphite, due to its layered structure, is capable for reversible electrochemical intercalation from lithium non-aqueous solutions. The energy density of modern LIBs is 150-200 W•h/kg, close to the limit created by the existing electrochemical system., More intensive research is required to find new electrode materials for creating LIBs of the next generation, with higher electrochemical performance. Using nanotechnologies makes it possible to create materials with higher performance. There is reason to believe that anodes created with nanomaterials based on silicon or tin, as the replacement for graphite, will significantly improve the electrochemical performance of LIBs completely. Additionally, a list of promising cathode materials should include lithiated iron phosphate. In the future, we can highlight three electrochemical systems as promising batteries: lithium-air batteries, lithium-sulfur batteries and sodium-ion batteries. The review is showing the contribution of Russian scientists to the development of chemical current sources with anodes based on lithium.