Carbon nanofibers with diameters that fall into submicron and nanometer range have attracted growing attention in recent years due to their superior chemical, electrical, and mechanical properties in combination with their unique 1D nanostructures. Unlike catalytic synthesis, electrospinning polyacrylonitrile (PAN) followed by stabilization and carbonization has become a straightforward and convenient route to make continuous carbon nanofibers. This paper is a comprehensive and state-of-the-art review of the latest advances made in development and application of electrospun PAN-based carbon nanofibers. Our goal is to demonstrate an objective and overall picture of current research work on both functional carbon nanofibers and high-strength carbon nanofibers from the viewpoint of a materials scientist. Strategies to make a variety of carbon nanofibrous materials for energy conversion and storage, catalysis, sensor, adsorption/separation, and biomedical applications as well as attempts to achieve high-strength carbon nanofibers are addressed.