Carbon foams are hypothetical carbon allotropes that contain graphene (sp 2carbon) segments, connected by sp 3carbon atoms, resulting in porous structures. These structures may represent novel stable carbon modifications with sp 2+ sp 3hybridization. Carbon foams show high structural stability at very low mass density. The construction principles, the structures, the energetics as well as the electronic and mechanical properties of carbon foams is discussed. The study is restricted to foam structures with sixfold rings and hexagonal cross-sections (hexagon preserving foams). The relation to defected graphite and the so-called Glitter structures is briefly discussed. The similarity of electronic band structure and the electronic DOS (density of states) of foams to carbon nanotubes is explained.