The new term of the U.S. Supreme Court begins today, October 7th. Deemed essential, the court is currently operating normally. However, a notice on their website indicates that this decision will be revisited if the appropriation lapse lasts beyond October 11th.
During the term you can keep up with case developments using the Court's online docket search or follow updates and analysis from SCOTUSblog.
Image by Daderot (Own work) [Public domain], via Wikimedia Commons