In biochemistry, a nuclease (also archaically known as nucleodepolymerase or polynucleotidase) is an enzyme capable of cleaving the phosphodiester bonds that link nucleotides together to form nucleic acids. Nucleases variously affect single and double stranded breaks in their target molecules. In living organisms, they are essential machinery for many aspects of DNA repair. Defects in certain nucleases can cause genetic instability or immunodeficiency. Nucleases are also extensively used in molecular cloning.

There are two primary classifications based on the locus of activity. Exonucleases digest nucleic acids from the ends. Endonucleases act on regions in the middle of target molecules. They are further subcategorized as deoxyribonucleases and ribonucleases. The former acts on DNA, the latter on RNA.

In the late 1960s, scientists Stuart Linn and Werner Arber isolated examples of the two types of enzymes responsible for phage growth restriction in Escherichia coli (E. coli) bacteria. One of these enzymes added a methyl group to the DNA, generating methylated DNA, while the other cleaved unmethylated DNA at a wide variety of locations along the length of the molecule. The first type of enzyme was called a "methylase" and the other a "restriction nuclease". These enzymatic tools were important to scientists who were gathering the tools needed to "cut and paste" DNA molecules. What was then needed was a tool that would cut DNA at specific sites, rather than at random sites along the length of the molecule, so that scientists could cut DNA molecules in a predictable and reproducible way.

An important development came when H.O. Smith, K.W. Wilcox, and T.J. Kelly, working at Johns Hopkins University in 1968, isolated and characterized the first restriction nuclease whose functioning depended on a specific DNA nucleotide sequence. Working with Haemophilus influenzae bacteria, this group isolated an enzyme, called HindII, that always cut DNA molecules at a particular point within a specific sequence of six base pairs. They found that the HindII enzyme always cuts directly in the center of this sequence (between the 3rd and 4th base pairs).

Most nucleases are classified by the Enzyme Commission number of the "Nomenclature Committee of the International Union of Biochemistry and Molecular Biology" as hydrolases (EC-number 3). The nucleases belong just like phosphodiesterase, lipase and phosphatase to the esterases (EC-number 3.1), a subgroup of the hydrolases. The esterases to which nucleases belong are classified with the EC-numbers 3.1.11 - EC-number 3.1.31.

Nuclease primary structure is by and large poorly conserved and minimally conserved at active sites, the surfaces of which primarily comprise acidic and basic amino acid residues. Nucleases can be classified into folding families.

A nuclease must associate with a nucleic acid before it can cleave the molecule. That entails a degree of recognition. Nucleases variously employ both nonspecific and specific associations in their modes of recognition and binding. Both modes play important roles in living organisms, especially in DNA repair.

Nonspecific endonucleases involved in DNA repair can scan DNA for target sequences or damage. Such a nuclease diffuses along DNA until it encounters a target, upon which the residues of its active site interact with the chemical groups of the DNA. In the case of endonucleases such as EcoRV, BamHI, and PvuII, this nonspecific binding involves electrostatic interactions between minimal surface area of the protein and the DNA. This weak association leaves the overall shape of the DNA undeformed, remaining in B-form.