Among RNA viruses, the order Nidovirales stands out for including viruses with the largest RNA genomes currently known. Nidoviruses employ a complex RNA-synthesizing machinery comprising a variety of non-structural proteins (nsps). One of the postulated drivers of the expansion of nidovirus genomes is the presence of a proofreading 3′-to-5′ exoribonuclease (ExoN) belonging to the DEDDh family. ExoN may enhance the fidelity of RNA synthesis by correcting nucleotide incorporation errors made by the RNA-dependent RNA polymerase. Here, we review our current understanding of ExoN evolution, structure, and function. Most experimental data are derived from studies of the ExoN domain of coronaviruses (CoVs), which were triggered by the bioinformatics-based identification of ExoN in the genome of severe acute respiratory syndrome coronavirus (SARS-CoV) and its relatives in 2003. Although convincing data supporting the proofreading hypothesis have been obtained, from biochemical assays and studies with CoV mutants lacking ExoN functionality, the features of ExoN from most other nidovirus families remain to be characterized. Remarkably, viable ExoN knockout mutants were obtained only for two CoVs, mouse hepatitis virus (MHV) and SARS-CoV, whose RNA synthesis and replication kinetics were mildly affected by the lack of ExoN function. In several other CoV species, ExoN inactivation was not tolerated, and knockout mutants could not be rescued when launched using a reverse genetics system. This suggests that ExoN is also critical for primary viral RNA synthesis, a property that poorly matches the profile of an enzyme that would merely boost long-term replication fidelity. In CoVs, ExoN resides in a bifunctional replicase subunit (nsp14) whose C-terminal part has (N7-guanine)-methyltransferase activity. The crystal structure of SARS-CoV nsp14 has shed light on the interplay between these two domains, and on nsp14’s interactions with nsp10, a co-factor that strongly enhances ExoN activity in vitro assays. Further elucidation of the structure-function relationships of ExoN and its interactions with other (viral and/or host) members of the CoV replication machinery will be key to understanding the enzyme’s role in viral RNA synthesis and pathogenesis, and may contribute to the design of new approaches to combat emerging nidoviruses.