Exonucleases are enzymes that work by cleaving nucleotides one at a time from the end (exo) of a polynucleotide chain. A hydrolyzing reaction that breaks phosphodiester bonds at either the 3′ or the 5′ end occurs. Its close relative is the endonuclease, which cleaves phosphodiester bonds in the middle (endo) of a polynucleotide chain. Eukaryotes and prokaryotes have three types of exonucleases involved in the normal turnover of mRNA: 5′ to 3′ exonuclease (Xrn1), which is a dependent decapping protein; 3′ to 5′ exonuclease, an independent protein; and poly(A)-specific 3′ to 5′ exonuclease.
RNA polymerase II is known to be in effect during transcriptional termination; it works with a 5' exonuclease (human gene Xrn2) to degrade the newly formed transcript downstream, leaving the polyadenylation site and simultaneously shooting the polymerase. This process involves the exonuclease's catching up to the pol II and terminating the transcription.
Pol I then synthesizes DNA nucleotides in place of the RNA primer it had just removed. DNA polymerase I also has 3' to 5' and 5' to 3' exonuclease activity, which is used in ing and proofreading DNA for errors. The 3' to 5' can only remove one mononucleotide at a time, and the 5' to 3' activity can remove mononucleotides or up to 10 nucleotides at a time.
In 1971, Lehman IR discovered exonuclease I in E. coli. Since that time, there have been numerous discoveries including: exonuclease, II, III, IV, V, VI, VII, and VIII. Each type of exonuclease has a specific type of function or requirement.
Exonuclease I breaks apart single-stranded DNA in a 3' → 5' direction, releasing deoxyribonucleoside 5'-monophosphates one after another. It does not cleave DNA strands without terminal 3'-OH groups because they are blocked by phosphoryl or acetyl groups. 
Exonuclease II is associated with DNA polymerase I, which contains a 5' exonuclease that clips off the RNA primer contained immediately upstream from the site of DNA synthesis in a 5' → 3' manner.
Exonuclease III has four catalytic activities:
Exonuclease IV adds a water molecule, so it can break the bond of an oligonucleotide to nucleoside 5' monophosphate. This exonuclease requires Mg 2+ in order to function and works at higher temperatures than exonuclease I.
Exonuclease V is a 3' to 5' hydrolyzing enzyme that catalyzes linear double-stranded DNA and single-stranded DNA, which requires Ca2+. This enzyme is extremely important in the process of homologous recombination.
Exonuclease VIII is 5' to 3' dimeric protein that does not require ATP or any gaps or nicks in the strand, but requires a free 5' OH group to carry out its function.
The 3' to 5' human type endonuclease is known to be essential for the proper processing of histone pre-mRNA, in which U7 snRNP directs the single cleavage process. Following the removal of the downstream cleavage product (DCP) Xrn1 continues to further breakdown the product until it is completely degraded. This allows the nucleotides to be recycled. Xrn1 is linked to a co-transcriptional cleavage (CoTC) activity that acts as a precursor to develop a free 5' unprotected end, so the exonuclease can remove and degrade the downstream cleavage product (DCP). This initiates transcriptional termination because one does not want DNA or RNA strands building up in their bodies.
CCR4-Not is a general transcription regulatory complex in budding yeast that is found to be associated with mRNA metabolism, transcription initiation, and mRNA degradation. CCR4 has been found to contain RNA and single-stranded DNA 3' to 5' exonuclease activities. Another component associated with the CCR4-Not is CAF1 protein, which has been found to contain 3' to 5' or 5' to 3' exonuclease domains in the mouse and Caenorhabditis elegans. This protein has not been found in yeast, which suggests that it is likely to have an abnormal exonuclease domain like the one seen in a metazoan. Yeast contains Rat1 and Xrn1 exonuclease. The Rat1 works just like the human type (Xrn2) and Xrn1 function in the cytoplasm is in the 5' to 3' direction to degrade RNAs (pre-5.8s and 25s rRNAs) in the absence of Rat1.
In beta Coronaviruses, including SARS-CoV-2, a proof reading exonuclease, nsp14-ExoN, that is part of the viral genome, is responsible for recombination that is implicated in novel strain emergence.