A lithium-ion battery anode layer, comprising an anode active material embedded in pores of a solid graphene foam composed of multiple pores and pore walls, wherein (a) the pore walls contain a pristine graphene material having essentially no (less than 0.01%) non-carbon elements or a non-pristine graphene material having 0.01% to 5% by weight of non-carbon elements; (b) the anode active material is in an amount from 0.5% to 95% by weight based on the total weight of the graphene foam and the anode active material combined, and (c) some of the multiple pores are lodged with particles of the anode active material and other pores are particle-free, and the graphene foam is sufficiently elastic to accommodate volume expansion and shrinkage of the particles of the anode active material during a battery charge-discharge cycle to avoid expansion of the anode layer. Preferably, the solid graphene foam has a density from 0.01 to 1.7 g/cm3, a specific surface area from 50 to 2,000 m2/g, a thermal conductivity of at least 100 W/mK per unit of specific gravity, and/or an electrical conductivity no less than 1,000 S/cm per unit of specific gravity.