For transcription elongation, all cellular RNA polymerases form a stable elongation complex (EC) with the DNA template and the RNA transcript. Since the millennium, a wealth of structural information and complementary functional studies provided a detailed three-dimensional picture of the EC and many of its functional states. Here we summarize these studies that elucidated EC structure and maintenance, nucleotide selection and addition, translocation, elongation inhibition, pausing and proofreading, backtracking, arrest and reactivation, processivity, DNA lesion-induced stalling, lesion bypass, and transcriptional mutagenesis. In the future, additional structural and functional studies of elongation factors that control the EC and their possible allosteric modes of action should result in a more complete understanding of the dynamic molecular mechanisms underlying transcription elongation. This article is part of a Special Issue entitled: RNA polymerase II Transcript Elongation.