The death penalty—also known as capital punishment—refers to the process of state and federal courts sentencing persons convicted of the most serious criminal offenses (capital offenses or capital crimes) to death. The specific crimes and circumstances for which the death penalty is a potential punishment (usually murder) are defined by state and federal statutes enacted by state legislatures and the United States Congress, respectively.

These death penalty or capital punishment statutes are often located in the penal or criminal code, and often in the same statute that defines a criminal offense such as murder. Twenty-two states and the District of Columbia do not have the death penalty as a potential punishment for any criminal offense.

In the state of New Mexico, the death penalty has been abolished. New Mexico repealed the death penalty in 2009, replacing it with the sentence of life imprisonment without the possibility of parole for crimes that would have previously been eligible for capital punishment. This change in law means that for any crimes committed after July 1, 2009, the state does not impose the death penalty. However, the repeal was not retroactive, which means that inmates who were sentenced to death before the abolition could still be on death row or have their sentences carried out. It's important to note that while New Mexico state law does not permit the death penalty, federal law still allows for capital punishment, and thus individuals in New Mexico could potentially face the death penalty for federal crimes.