Exemplary embodiments provide methodologies for generating structures of filamentous carbon (or carbon filaments) with controlled geometries. In one exemplary embodiment of forming the carbon filament structure, a metal template can be exposed to a fuel rich gaseous mixture to form a carbon filament structure at an appropriate gas flow and/or at an appropriate temperature on the metal template. The metal template can have one or more metal surfaces with controlled geometries. Carbon filament structures can then be grown on the metal surfaces having corresponding geometries (or shapes) in the growth direction. The carbon filament structure can be two or three dimensional and can have high density. In various embodiments, the metal template can be removed to leave a self-supporting carbon filament structure.