Fast charging is considered to be a key requirement for widespread economic success of electric vehicles. Current lithium‐ion batteries (LIBs) offer high energy density enabling sufficient driving range, but take considerably longer to recharge than traditional vehicles. Multiple properties of the applied anode, cathode, and electrolyte materials influence the fast‐charging ability of a battery cell. In this review, the physicochemical basics of different material combinations are considered in detail, identifying the transport of lithium inside the electrodes as the crucial rate‐limiting steps for fast‐charging. Lithium diffusion within the active materials inherently slows down the charging process and causes high overpotentials. In addition, concentration polarization by slow lithium‐ion transport within the electrolyte phase in the porous electrodes also limits the charging rate. Both kinetic effects are responsible for lithium plating observed on graphite anodes. Conclusions drawn from potential and concentration profiles within LIB cells are complemented by extensive literature surveys on anode, cathode, and electrolyte materials—including solid‐state batteries. The advantages and disadvantages of typical LIB materials are analyzed, resulting in suggestions for optimum properties on the material and electrode level for fast‐charging applications. Finally, limitations on the cell level are discussed briefly as well.