Exonucleases are key enzymes involved in many aspects of cellular metabolism and maintenance and are essential to genome stability, acting to cleave DNA from free ends. Exonucleases can act as proofreaders during DNA polymerisation in DNA replication, to remove unusual DNA structures that arise from problems with DNA replication fork progression, and they can be directly involved in repairing damaged DNA. Several exonucleases have been recently discovered, with potentially critical roles in genome stability and ageing. Here we discuss how both intrinsic and extrinsic exonuclease activities contribute to the fidelity of DNA polymerases in DNA replication. The action of exonucleases in processing DNA intermediates during normal and aberrant DNA replication is then assessed, as is the importance of exonucleases in repair of double-strand breaks and interstrand crosslinks. Finally we examine how exonucleases are involved in maintenance of mitochondrial genome stability. Throughout the review, we assess how nuclease mutation or loss predisposes to a range of clinical diseases and particularly ageing.