Disclosed here are processes for preparing carbonized polymers (preferably carbon fibers), comprising sulfonating a polymer with a sulfonating agent that comprises SO3 dissolved in a solvent to form a sulfonated polymer; treating the sulfonated polymer with a heated solvent, wherein the temperature of the solvent is at least 95° C.; and carbonizing the resulting product by heating it to a temperature of 500-3000° C. Carbon fibers made according to these methods are also disclosed herein.