In the U.S. Senate, the filibuster allows a single senator to effectively block a vote by way of the senate rules that allow for unlimited debate, but now, the senate rules have somehow been modified so that to invoke filibuster you don't even need to actually have 'debate' where you do silly things like read names from the telephone book to keep the debate going. How have the senate rules been changed to allow for a filibuster without continued debate?
It is true that at one point you did have to talk continuously to block a vote, but it hasn't been true for ages. Skip a few paragraphs if you don't care about the history:
Originally, the Senate had a way for the majority to vote to end debate on a matter, by voting that it's time to vote (yes, really) on the matter at hand. In 1806 the President of the Senate (Aaron Burr) suggested that the Senate eliminate this option because it was hardly ever used. According to The Previous Question: Its Standing as a Precedent for Cloture in the United States Senate, Burr:
mentioned one or two rules which appeared to him to need a revisal, and recommended the abolition of that respecting the previous question [the call to vote], which he said had in the four years been only once taken, and that upon an amendment. This was proof that it could not be necessary
The Senate agreed and eliminated this option from their rules, which now made unbreakable filibusters possible; they didn't actually happen for a few decades. During WWI a Senate filibuster blocked one of President Wilson's proposals, and he decided enough was enough and moved for a way to override filibusters.
In 1917 the Senate voted to allow cloture by a two-thirds majority vote (it was changed to three-fifths later). As a side-effect of this, there was now no need to hold the floor by talking, because the filibustering side can just vote against cloture indefinitely. They don't even need to be present, there just needs to be enough of them absent to prevent a cloture motion from passing; one representative needs to hang around to suggest the absence of a quorum, and that's it.
There have been "real" filibusters since 1917, like Strom Thurmond's famous Civil Rights Act filibuster, but those were largely for show or to make a point. It hasn't been necessary to hold the floor by talking since 1917