This paper is a review of results on Artinian, perfect, and semiprimary semigroup rings. A complete characterization is obtained for the right perfect and semiprimary contracted semigroup rings with an arbitrary coefficient ring. We give another proof Zelmanov's theorem which states the finiteness of the semigroup of an Artinian semigroup ring. The sufficient conditional for a semigroup, ring to be left artinian are considerd.All the statements given with complete proofs. Some profs are modernized.