"Regular" PGA Tour events are cut after 36 holes to the low 70 scores plus ties. If that results in more than 78 golfers making the cut, then another cut takes place after 54 holes, again to the low 70 plus ties.

("Regular" PGA Tour events are those tournaments that are not majors, not World Golf Championships events, and not short-field events. Majors have their own cut policies - see links below - and WGC tournaments do not have cuts.

The PGA Tour's winners-only season-opener also does not have a cut.)

The PGA Tour cut rule last changed in 2008, when the tour introduced what came to be known as "Rule 78," a rule that proved quite controversial. So controversial that little more than a month after Rule 78 was first applied, the PGA Tour Policy Board voted to change it. The result was the PGA Tour cut that exists today, as described in the first paragraph above. (You can find more info about Rule 78 in our explanation of MDF, the acronym now used to designate golfers who make the 36-hole cut but not the 54-hole one.)
As noted, major championships have their own cut rules (as do the other professional tours). For those rules, see:

• Masters cut
• U.S. Open cut
• British Open cut
• PGA Championship cut

See also:
What does 'MDF' in golf scores mean?