Methods for producing porous carbon product utilize template material in the form of template particles containing macropores and a polymerizable carbon precursor substance. The macropores of the template are infiltrated with the precursor substance in dissolved or melted form. After carbonization of the infiltrated precursor substance, the template is removed to form the porous carbon product. In order to obtain a carbon structure with hierarchical porosity having a high fraction of mesopores having pore sizes in the range of 2 to 50 nm, after the infiltration and before carbonization, the precursor substance within the macropores of the template is subjected to a treatment at a foaming temperature at which the precursor substance foams under polycondensation and fills the macropores as substantially mesoporous foam, in which at least 70% of the pores have pore sizes in the range of 10 to 150 nm.