Smith v. Greenhow was a United States Supreme Court case that dealt with the issue of whether a state court had the authority to issue a writ of habeas corpus to a prisoner held in federal custody. The case arose when the petitioner, Smith, was arrested by federal officers and held in federal custody. Smith then filed a petition for a writ of habeas corpus in a state court, seeking to be released from federal custody. The state court granted the writ, and the federal officers refused to comply. The Supreme Court held that the state court did not have the authority to issue the writ of habeas corpus. The Court reasoned that the writ of habeas corpus is a federal prerogative, and that the state court did not have the authority to interfere with the federal government's power to detain a prisoner. The Court also noted that the writ of habeas corpus is a fundamental right, and that the federal government has the exclusive power to determine when and how it should be used. In conclusion, 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 federal custody. The Court reasoned that the writ of habeas corpus is a federal prerogative, and that the state court did not have the authority to interfere with the federal government's power to detain a prisoner.

Justice Field delivered the dissenting opinion in Smith v. Greenhow, arguing that the Court should have affirmed the judgment of the Circuit Court for Virginia. He argued that under Virginia law, a contract was formed when an offer was accepted and consideration given; here, there had been both an offer and acceptance as well as consideration paid by Smith to Greenhow. Furthermore, he noted that it would be unjust to allow one party to repudiate their obligations after having received payment from another party without any legal justification or excuse. As such, Justice Field concluded that since no fraud or mistake had been alleged on behalf of either party in this case and all elements necessary for a valid contract were present at its formation, then it must be enforced according to its terms regardless of whether it is considered fair or not.