Porous three-dimensional networks of polyurea and porous three-dimensional networks of carbon and methods of their manufacture are described. In an example, polyurea aerogels are prepared by mixing an triisocyanate with water and a triethylamine to form a sol-gel material and supercritically drying the sol-gel material to form the polyurea aerogel. Subjecting the polyurea aerogel to a step of pyrolysis may result in a three dimensional network having a carbon skeleton, yielding a carbon aerogel. The density and morphology of polyurea aerogels can be controlled by varying the amount of isocyanate monomer in the initial reaction mixture. A lower density in the aerogel gives rise to a fibrous morphology, whereas a greater density in the aerogel results in a particulate morphology. Polyurea aerogels described herein may also exhibit a reduced flammability.