Methods of forming solid carbon products include disposing a plurality of nanotubes in a press, and applying heat to the plurality of carbon nanotubes to form the solid carbon product. Further processing may include sintering the solid carbon product to form a plurality of covalently bonded carbon nanotubes. The solid carbon product includes a plurality of voids between the carbon nanotubes having a median minimum dimension of less than about 100 nm. Some methods include compressing a material comprising carbon nanotubes, heating the compressed material in a non-reactive environment to form covalent bonds between adjacent carbon nanotubes to form a sintered solid carbon product, and cooling the sintered solid carbon product to a temperature at which carbon of the carbon nanotubes do not oxidize prior to removing the resulting solid carbon product for further processing, shipping, or use.