In Peralta v. United States, the Supreme Court held that a federal court had jurisdiction to hear an appeal from a decision of the District Court for California in which it was determined that certain lands belonged to Mexico and not to the United States. The case arose out of a dispute between two Mexican citizens, Francisco Peralta and Jose Antonio Estudillo, over ownership of land located in what is now San Diego County, California. Estudillo claimed title under grants made by Spanish authorities prior to 1821 when Mexico gained independence from Spain; Peralta argued he acquired title through adverse possession after 1848 when the Treaty of Guadalupe Hidalgo ceded much of present-day California (including San Diego) from Mexico to the U.S., thus making him owner by virtue of his occupancy since then. The Supreme Court found that while Congress had exclusive power over territories belonging or ceded to it, this did not extend so far as depriving individuals who were already owners before such acquisition took place their right or interest therein without due process according law; therefore they concluded that Estudillo's claim should be heard in federal court on its merits rather than dismissed outright as being outside its jurisdiction because it involved pre-1848 claims arising within territory subsequently acquired by treaty with another nation.

In Peralta v. United States, the Supreme Court was tasked with determining whether a Spanish land grant in California could be confirmed by an American court of equity. The majority opinion held that it could not because the treaty between Spain and America did not provide for such confirmation, but Justice Field dissented from this decision. He argued that since Congress had passed legislation to confirm certain grants made before 1848, there was no reason why they should not also confirm those granted after 1848 as well. Furthermore, he noted that if these grants were allowed to remain unconfirmed then it would create great hardship on many settlers who had relied upon them when purchasing their lands or making improvements thereto. Thus, Justice Field concluded that Congress should have been given more latitude in deciding how to handle these cases and urged his colleagues to reconsider their ruling so as to allow for greater flexibility in confirming Spanish land grants in California going forward.