The current status and development of petroleum residue upgrading via coking in Russia and over the world have been surveyed with an emphasis on the role of the process in salving the problem of increasing the refining depth. Theoretical concepts of thermal conversion of heavy petroleum feedstock and the structure of asphaltenes as principal coke-forming compounds have been discussed, the results of studies on the formation of coke as either a byproduct or (to a greater extent) the desired product have been considered, and models of the coke structure have been proposed. The characteristic features of the coking process for petroleum residues of various chemical compositions have been addressed, as well as means for controlling the feedstock thermal stability and the yield and quality of coke with the use of external factors.