Can reject/approve by a 2/3 vote -> 2012 rejected the UN Convention on the Rights of Persons with Disabilities, rejected Versailles
Can be circumvented by executive agreements - outnumber treaties 10:1 since 1942
Approves appointments
Confirms nominees put forward by the President to federal courts, the cabinet and ambassadorial posts
Entails hearings and a vote
Tries impeachment cases
Senate removes the president/official/justice if 2/3 agree -> Clinton and Trump impeached but not removed from offic, Nixon resigned out of fear of impeachment
Elects the vice president if the Electoral college is deadlocked

Hasn't happened since 1824
Majority leader is fourth in line to the presidency
Filibuster
Action designed to prolong debate and delay or prevent a vote on a bill, resolution, amendment, or other debatable question.
Can filibuster things like gun control and healthcare reforms
1917 - Senator Follette to demand free speech during wartime
1930s - Senator Long used filibuster against bills he thought favoured the rich over the poor
Thurmond - longest filibuster against the Civil Rights Act of 1957, 24 hours and 18 minutes