Criminal jurisdiction is a term used in constitutional law and public law to describe the power of courts to hear a case brought by a state accusing a defendant of the commission of a crime. It is relevant in three distinct situations:

Under the public international law system, de jure states are sovereign within their own territorial boundaries. A few states such as the Netherlands have adopted a monist approach, i.e. they accept international and municipal laws as part of a single system. Thus, whether a supranational court or tribunal has criminal jurisdiction over its territory or citizens, will be determined by international law. The majority of states are dualist, i.e. they will only accept international obligations through the process of incorporation, say by signing and adopting treaties and conventions. Hence, whether a supranational court or tribunal will have jurisdiction and, if so, over what subject matter and over what period of time, will be decided by the sovereign government of the day.

Because each government is supreme, it can enact whatever statutes it wishes. Thus, State A would have the power to make a law which, for example, made it an offence to smoke in the streets of State B, a neighbouring state. State A could employ officers and equip them with cameras. These officers could then collect evidence in State B and, when its citizens returned home, State A could prosecute them for breach of the law. But State A's law could not be directly effective in State B because that would make State B less than sovereign. Similarly, State A could not seek the extradition of its own citizens from State B unless State B was formally to consent (usually through the negotiation of a treaty including the particular offence).

Transborder crimes take place in more than one state. For example, a defendant may fire a gun, post a package, or write or speak words in State A, but the effects of each action are felt in State B. Some states claim a public policy justification to exercise jurisdiction over crimes committed by, or crimes committed against their citizens, even though these crimes are committed outside their borders. Thus, one of the classifications of crime is "crimes against the state". These are crimes that affect the interests of the state or its administration. In extreme cases, a state may wish to prosecute one of its own citizens for treason even though all the relevant acts and omissions took place in another state. Similarly, if a citizen of State A is acting in a way that interferes with the friendly relations between State A and State B, it may be expedient to prosecute this citizen no matter where the relevant acts have been committed. Jurisdiction may also be claimed over crimes on board the ships and aircraft operated by corporations based in the given state, no matter where these craft may be located at the relevant time. In English law, where murder and manslaughter are concerned, the English court has jurisdiction over offences committed abroad, if committed by a British citizen (see section 9 of the Offences against the Person Act 1861 and section 3 of the British Nationality Act 1948). In R v Cheong (2006) AER (D) 385 the appellant was living in Guyana in 1983. He shot and killed a man who had just robbed his wife and sister-in-law. Under local law he was charged only with the unlicensed possession of a firearm; but as a British citizen, section 9 of the 1861 Act applied 19 years after he returned to England and he was charged with murder. On appeal, a conviction for manslaughter was upheld. At a level of conventional policy, there are two main theories to justify the exercise of jurisdiction:

The state in which the sequence of events begins, claims jurisdiction because the accused did everything in his or her power to commit the offence within its territory. Intending to deceive Y into parting with money, X writes a begging letter claiming to be a penniless widow with ten starving children and posts it in State A. X must then rely on the postal workers to carry the letter to Y in State B. No matter how hard X tries, X cannot take any further action to promote the scheme, and whether it succeeds or fails is entirely outside his or her ability to control. There are three theoretical issues to consider:

In English law, see the definition of a deception which must be the operative cause of the "obtaining" in the deception offences and under the Theft Act 1978, and note that all the inchoate offencess move in time and across borders so that an attempt continues from the proximate act until failure, a conspiracy agreement is not limited to a particular place, and the encouragement by a secondary party as an accessory continues until the principal commits the substantive offence.

If the injury or damage affects a citizen within the territory of a state, it would be usual for that state to claim jurisdiction to protect the interests of those who are present within its borders. But X would not have taken any action within State B's borders, so the wording of the actus reus must permit a prosecution in this situation. The theoretical justification for this jurisdiction may be that X has intended to cause the loss or injury and so should not escape liability through the device of only seeking to deceive those resident outside State A (a strategy that would be very simple given the internet). The justification is less clear when the place of injury is an accident. Within a single state, the doctrine of transferred intent would apply to criminalise accidental departures from a planned attack, but if X's letter is redirected out of State A by one of Y's helpful relatives, the receipt of the letter by Y on holiday in State B is entirely outside X's actual intention (just it might be irrelevant to a sender where the recipient of an e-mail is resident). Alternatively, suppose that X physically attacks Y in State A, intending to kill him. Both are nationals of State A. Y is seriously injured and, because the hospitals in State B have a superior track record for treating injuries of this type, Y arranges to be transferred to State B where he later dies. Again, there is no causal connection between X's initial criminal acts and the territory of State B, and seeking to found jurisdiction simply on the ground that Y died within its borders, is not wholly convincing given that Y is not a national of State B and so neither owes allegiance nor is owed any duty of protection as a part of State B's social contract.

The United States is a federation of states. The U.S. Constitution creates a federal government and legislature that has general powers over the territory of the whole and over foreign policy, whereas the individual states have their own governments that, within the scope allowed by the federal constitution, have local territorial jurisdiction. There is a system of federal courts which have jurisdiction to hear charges alleging federal crimes, and state courts have jurisdiction to hear charges alleging violations of local state law.