Courts throughout the country are shutting down, postponing a case load of trials. Those that haven't shuttered all together are generally implementing strict protocols to keep people safe.
Check out us.courts.gov to keep track of various federal court orders. A few examples include:
In the U.S. District Court for the Northern District of Illinois, which includes Chicago, proceedings are being postponed, with filing deadlines being extended accordingly.
The U.S. Supreme Court justices will work from home. Filing deadlines have not been extended.
As of March 17th, the Ninth Circuit has closed to the public, and oral arguments are being determined on a case-by-case basis, in some cases holding argument via telephone or video. Filing deadlines will be extended on an “as needed" basis.
Of course, these are just a few examples of the various approaches federal courts are using. This is a developing situation with many unknown answers at the moment.