Driving endonuclease genes (DEGs) spread through a population by a non-Mendelian mechanism. In a heterozygote,
the protein encoded by a DEG causes a double-strand break in the homologous chromosome opposite to where its
gene is inserted and when the break is repaired using the homologue as a template the DEG heterozygote is converted
to a homozygote. Some DEGs occur naturally while several classes of endonucleases can be engineered to spread in this
way, with CRISPR-Cas9 based systems being particularly flexible. There is great interest in using driving endonuclease
genes to impose a genetic load on insects that vector diseases or are economic pests to reduce their population density,
or to introduce a beneficial gene such as one that might interrupt disease transmission. This paper reviews both the
population genetics and population dynamics of DEGs. It summarises the theory that guides the design of DEG constructs
intended to perform different functions. It also reviews the studies that have explored the likelihood of resistance to DEG
phenotypes arising, and how this risk may be reduced. The review is intended for a general audience and mathematical
details are kept to a minimum.