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 Wyoming, the death penalty, or capital punishment, is a legal penalty. The state's statutes specify that capital punishment can be applied to certain cases of first-degree murder under specific aggravating circumstances. These circumstances are outlined in the state's penal code and must be proven beyond a reasonable doubt for the death penalty to be considered as a sentencing option. The method of execution in Wyoming is lethal injection. However, if lethal injection is found to be unconstitutional or is otherwise unavailable, the state allows for the use of a gas chamber as an alternative method. It's important to note that the application of the death penalty is subject to constitutional constraints, and cases involving capital punishment often undergo extensive judicial review to ensure that the application of the death penalty is consistent with both state and federal constitutions.