Walker v. United States was a Supreme Court case that addressed the issue of whether a federal court had the authority to issue a writ of habeas corpus to a prisoner held in a military prison. The case arose when a prisoner, William Walker, was held in a military prison in Washington, D.C. after being convicted of desertion from the Union Army. Walker sought a writ of habeas corpus from a federal court, arguing that he was being unlawfully detained. The Supreme Court held that the federal court did not have the authority to issue a writ of habeas corpus to a prisoner held in a military prison. The Court reasoned that the writ of habeas corpus was a civil remedy, and that the military had exclusive jurisdiction over military prisoners. The Court also noted that the writ of habeas corpus was not available to prisoners held in military prisons, as the writ was intended to protect citizens from unlawful detention by the government. The Court's decision in Walker v. United States established that the writ of habeas corpus was not available to prisoners held in military prisons. This decision has been cited in subsequent cases involving the rights of military prisoners.

In Walker v. United States, the Supreme Court was tasked with determining whether a federal tax on distilled spirits was constitutional. The majority opinion held that it was, but Justice Swayne dissented from this ruling and argued that Congress had exceeded its authority under the Constitution by imposing such a tax without apportionment among the states according to population. He reasoned that since taxation is an exercise of power delegated to Congress by the people through their state governments, any taxes must be imposed in proportion to each state's representation in Congress as determined by population size. Since this particular tax did not meet these criteria, he concluded it violated Article I Section 2 Clause 3 of the Constitution and should therefore be declared unconstitutional.