Poly(A) polymerases were identified almost 50 years ago as enzymes that add multiple AMP residues to the 3' ends of primer RNAs without use of a template from ATP as cosubstrate and with release of pyrophosphate. Based on sequence homology of a signature motif in the catalytic domain, poly(A) polymerases were later found to belong to a superfamily of nucleotidyl transferases acting on a very diverse array of substrates. Enzymes belonging to the superfamily can add from single nucleotides of AMP, CMP or UMP to RNA, antibiotics and proteins but also homopolymers of many hundred residues to the 3' ends of RNA molecules. The recently reported structures of several nucleotidyl transferases facilitate the study of the catalytic mechanisms of these very diverse enzymes. Numerous structures of CCA-adding enzymes have now revealed all steps in the formation of a CCA tail at the 3' end of tRNAs. In addition, structures of poly(A) polymerases and uridylyl transferases are now available as binary and ternary complexes with incoming nucleotide and RNA primer. Some of these proteins undergo significant conformational changes after substrate binding. This is proposed to be an indication for an induced fit mechanism that drives substrate selection and leads to catalysis. Insights from recent structures of ternary complexes indicate an important role for the primer molecule in selecting the incoming nucleotide.