Craig v. Smith was a United States Supreme Court case that addressed the issue of whether a state court had the authority to issue a writ of habeas corpus to a prisoner who was being held in a federal prison. The case arose when a prisoner, William Craig, was held in a federal prison in the state of Missouri. Craig sought a writ of habeas corpus from the state court, claiming that he was being held in violation of his constitutional rights. The state court granted the writ, and the federal government appealed the decision to the Supreme Court. The Supreme Court held that the state court did not have the authority to issue a writ of habeas corpus to a prisoner held in a federal prison. The Court reasoned that the writ of habeas corpus was a federal remedy, and that the state court did not have the power to interfere with the federal government's authority to imprison individuals. The Court also noted that the writ of habeas corpus was a remedy that could only be used to challenge the legality of a prisoner's detention, and not to challenge the conditions of the prisoner's confinement. The Court's decision in Craig v. Smith established that state courts do not have the authority to issue writs of habeas corpus to prisoners held in federal prisons. The decision also clarified the scope of the writ of habeas corpus, and established that it could only be used to challenge the legality of a prisoner's detention, and not to challenge the conditions of the prisoner's confinement.

Justice Field delivered the dissenting opinion in Craig v. Smith, arguing that the majority's decision was contrary to established precedent and would have a detrimental effect on creditors' rights. He argued that under prior decisions of the Supreme Court, when an insolvent debtor has made a transfer of property with intent to defraud his creditors, such transfer is voidable by them even though it may be valid as between himself and third persons who are not parties to any fraud or collusion. In this case, he noted that there was evidence from which it could be inferred that Smith had transferred his property with fraudulent intent; thus, according to Field's interpretation of existing law at the time, Craig should have been allowed relief against him for recovery of her debt.