Abstract Carbon fibers are derived from carbonaceous compounds, such as polymers, through a decomposition process known as pyrolysis or carbonization. After this process, the carbon fibers are optionally graphitized by heating at temperatures much above that for carbonization. The most common precursors of carbon fibers are polyacrylonitrile (PAN) and pitch. The carbon in a carbon fiber is in the graphite family. However, unlike graphite, it is typically noncrystalline. Nevertheless, the sp2-hybridized atomic carbon layers in a carbon fiber are preferentially oriented along the fiber axis. As a consequence of the preferred orientation, a carbon fiber exhibits higher values of the strength, modulus, electrical conductivity, and thermal conductivity along the fiber axis than the transverse direction. The greater is the degree of preferred orientation, the higher are these values along the fiber axis. The properties of carbon fibers depend not only on the precursor material, but also on the heat-treatment temperature. The higher is the heat-treatment temperature, the greater is the degree of crystallographic order in the carbon. Carbon nanofibers (originally known as carbon filaments) and carbon nanotubes are much smaller in diameter than the conventional carbon fibers. Compared to conventional carbon fibers, they suffer from their discontinuous nature, limited degree of alignment, and limited degree of packing in a composite. The processing, structure, and properties of carbon fibers, carbon nanofibers, and carbon nanotubes are introduced.