Here's a brief post mortem.
In 1789, the first U.S. Senate adopted rules allowing the Senate to end debate and proceed to a vote. At the time Aaron Burr felt this was redundant, and a few years later the Senate agreed when it did not include a mechanism for ending debate when it rewrote the rules in 1806. This lack of ability to cut off debate laid the foundation for the use of the filibuster, although it took 31 years before the first filibuster was exercised.
In 1917 the Democratic Senate added a rule allowing for the cloture of debate (ending a filibuster) after a group of 12 anti-war senators blocked a bill that would have allowed President Wilson to arm merchant vessels to combat German submarine warfare. From 1917 to 1975, the requirement for cloture was two-thirds of those voting. In 1975 the Democratic-controlled Senate amended the rules so three-fifths of the senators sworn (usually 60 senators) could limit debate, except on votes to change Senate rules, which still required two-thirds to invoke cloture.
So with a two-thirds majority requirement for a rule change, how did the Senate manage to change the rule today?
Here's how filibuster expert Gregory Koger explained it to Ezra Klein today: