Polyadenylation is the non-template addition of adenosine nucleotides at the 3'-end of RNA, which occurs after transcription and generates a poly(A) tail up to 250-300 nucleotides long. In the first section of our review, we consider the classical process of mRNA 3'-terminus formation, which involves the cleavage of the transcript synthesized by RNA polymerase II and the associated poly(A) tail synthesis by canonical polyadenylate polymerase. Nucleotide sequences needed for mRNA cleavage and poly(A) tail synthesis, in particular the AAUAAA polyadenylation signal, as well as numerous proteins and their complexes involved in mRNA cleavage and polyadenylation, is described in detail. The significance of the poly(A) tail for prolonging mRNA lifetime and stimulating their translation is discussed. Data presented in the second section demonstrate that RNA transcribed by RNA polymerase III from certain SINEs (Short Interspersed Elements) can undergo AAUAAA-dependent polyadenylation. The structural and functional features of RNA polymerase III determine the unusual character of polyadenylation of RNAs synthesized by this enzyme. The history of recent developments in this area of study have been described in greater detail, in particular the discovery of AAUAAA-dependent polyadenylation of RNA synthesized by RNA polymerase III, which has not been discussed previously. Data on AAUAAA-independent polyadenylation catalyzed by noncanonical TRAMP poly(A)-polymerases (Trf4 and Trf5) have been presented in the third section. These enzymes promote rapid degradation of RNAs by adding a short poly(A) tail to them. This mechanism enables the recognition, poly(A)-marking, and elimination of incorrectly folded noncoding transcripts (e.g. ribosomal and transfer RNAs).