As for Members of Congress, rather than impeachment, the Constitution provides the remedy of “expulsion” in Article I, section 5: “Each House may determine the rules of its proceedings, punish its Members for disorderly behavior, and with the concurrence of two-thirds, expel a Member.” Only one chamber determines the fate of its own Members, with a 2/3 vote. Concurrence of the other body is not needed, so there is no trial.
Expulsions have been rare in congressional history because Members prefer to let constituents decide whether or not to remove a sitting Member by simply not re-electing him/her. In the Senate, 15 Senators have been expelled: 1 in 1797 and 14 for treason during the Civil War. In the House, 4 Representatives have been expelled - 3 for treason during the Civil War and 1 [Rep. Ozzie Meyers, D-PA] in 1980 for bribery [cash transfer caught on videotape by the FBI].
Some states have enacted “recall” election laws aimed at state level officials and legislators. Court rulings have established that Members of Congress, as federal constitutional officers, are not subject to recall under the authority of a state law. Nor is a recall special election procedure provided for in the U.S. Constitution for federal officials. Recall remains a state remedy. The removal of Members of the U.S. Congress is left to the expulsion clause of the Constitution, or to the wish of voters to hold them accountable for their actions by refusing to re-elect them in the next regular election.