On January 5, the U.S. Supreme Court agreed to hear Trump v Anderson, 23-719. Oral argument will be February 8. Briefs on the side of Trump are due January 18; briefs for the people who wanted to keep him off the Colorado presidential primary ballot are due January 31; any reply briefs are due February 5.
There were actually two cases in the U.S. Supreme Court on this subject. The first one was filed by the Colorado Republican Party, but a week later, when Trump filed his own case, it got its own separate docket number, so technically it is a separate case, and that is the case that the Court accepted.
Even though the case is being expedited, it is still not fast enough to change the Colorado Republican presidential primary ballots. They will contain Trump’s name, because when the Colorado Supreme Court ruled against him, it stayed its decision pending action by the U.S. Supreme Court. So the ballots will all have been printed with his name on them by the time the U.S. Supreme Court hears the case. Trump’s name is now on all ballots except the Maine primary ballot (and in Nevada, Trump did not file for the government-administered primary because instead he is competing in the Republican caucus).