An agreement between two or more people to commit an illegal act, along with an intent to achieve the agreement's goal. Most U.S. jurisdictions also require an overt act toward furthering the agreement. An overt act is a statutory requirement, not a constitutional one. See Whitfield v. United States, 453 U.S. 209 (2005). The illegal act is the conspiracy's "target offense."
Conspiracy generally carries a penalty on its own. In addition, conspiracies allow for derivative liability where conspirators can also be punished for the illegal acts carried out by other members, even if they were not directly involved. Thus, where one or more members of the conspiracy committed illegal acts to further the conspiracy's goals, all members of the conspiracy may be held accountable for those acts.
Where no one has actually committed a criminal act, the punishment varies. Some conspiracy statutes assign the same punishment for conspiracy as for the target offense. Others impose lesser penalties.