The Appointments Clause of the Constitution requires principal officers of the Executive Branch be nominated by the President and approved by the Senate. In United States v. Arthrex, Inc., the issue was whether Administrative Patent Judges (APJs), who issue decisions on the validity of patents on behalf of the Executive Branch, as appointed by the Secretary of Commerce, were constitutional. The Federal Circuit held that the appointments were unconstitutional because no principal officer could review APJ decisions, nor remove an APJ, and ordered that APJs be subsequently removable at will by the Secretary in order to make them inferior officers.
The Court, in a 5-4 decision by Chief Justice Roberts, agreed with the Federal Circuit that the nature of APJ authority made them principal officers that had to be appointed and confirmed under the Appointments Clause. However, the majority was split on how to rectify the issue. Justice Gorsuch argued in a concurrence that the proper approach was to simply vacate APJ rulings, while the other four ruled that decisions of APJs must be made reviewable by a principal officer. Justice Thomas, joined by Justices Breyer, Sotomayor, and Kagan, dissented, arguing that APJs were inferior officers low on the hierarchy in the Executive Branch, and their appointments by the Secretary were lawful. Justice Breyer, joined by Justices Sotomayor and Kagan, filed a separate dissent to further explain his support of Justice Thomas’ dissent, but also noting his agreement with the four-justice plurality’s choice of remedy given its decision on the constitutionality of the appointments.
A link to the opinion is here: https://www.supremecourt.gov/opinions/20pdf/19-1434_ancf.pdf