Somatic hypermutation (SHM) underlies the generation of a diverse repertoire of high-affinity antibodies. It is effected by a two-step process: (i) DNA lesions initiated by activation-induced cytidine deaminase (AID), and (ii) lesion repair by the combined intervention of DNA replication and repair factors that include mismatch repair (MMR) proteins and translesion DNA synthesis (TLS) polymerases. AID and TLS polymerases that are crucial to SHM, namely polymerase (pol) theta, pol zeta and pol eta, are induced in B cells by the stimuli that are required to trigger this process: B-cell receptor crosslinking and CD40 engagement by CD154. These polymerases, together with MMR proteins and other DNA replication and repair factors, could assemble to form a multimolecular complex ("mutasome") at the site of DNA lesions. Molecular interactions in the mutasome would result in a "polymerase switch", that is, the substitution of the high-fidelity replicative pol delta and pol epsilon with the TLS pol theta, pol eta, Rev1, pol zeta and, perhaps, pol iota, which are error-prone and crucially insert mismatches or mutations while repairing DNA lesions. Here, we place these concepts in the context of the existing in vivo and in vitro findings, and discuss an integrated mechanistic model of SHM.