In Lucia v. Securities and Exchange Commission [transcript, PDF] the court heard arguments on whether administrative law judges of the Securities and Exchange Commission (SEC) [official website] are officers of the United States within the meaning of the Appointments Clause [art. II, § 2, cl. 2]. If so, then they would have to be appointed by the commission rather than by SEC staff as is current practice. The US Court of Appeals for the District of Columbia Circuit ruled [opinion, PDF] that they are not officers of the United States.
In Pereira v. Sessions [transcript, PDF] the court heard arguments on whether, to trigger the stop-time rule for a non-permanent resident's eligibility for cancellation of removal [8 USC § 1229b(a) and (b)] by serving a "notice to appear," the government must "specify" the items listed in the definition of a "notice to appear," including "[t]he time and place at which the proceedings will be held."
In Chavez-Meza v. United States [transcript, PDF] the court heard arguments on whether, when a district court decides not to grant a proportional sentence reduction under 18 USC § 3582(c)(2) [text], it must provide some explanation for its decision when the reasons are not otherwise apparent from the record, or whether it can instead issue its decision without any explanation so long as it is issued on a preprinted form order containing the boilerplate language providing that the court has "tak[en] into account the policy statement set forth in 18 USSG § 1B1.10 and the sentencing factors set forth in 18 USC § 3553(a) [text], to the extent that they are applicable." Justice Neil Gorsuch is recused.