There have been 23 perfect games in baseball since 1901. A perfect game is when a pitcher pitches nine or more innings and doesn’t allow a baserunner.
The most famous almost-perfect game was pitched by Harvey Haddix of the Pirates in 1959. He threw 12 perfect innings but gave up hits in the 13th and lost the game.
In 1995, Pedro Martinez of the Expos threw nine perfect innings. He gave up a hit to the 28th batter in the 10th inning and was taken out of the game.
Armando Galarraga would have had a perfect game in 2010 if the umpire made a correct call in the ninth inning.
Dick Bosman is the only pitcher to miss a perfect game because of his own fielding error in a 1974 contest.
John Means of the Baltimore Orioles threw a no-hitter in 2021 that would have been a perfect game if the catcher had not dropped a third strike. He faced the minimum of 27 batters.
Carlos Rodon of the White Sox hit a batter in the 9th in a 2021 game. That was the only baserunner he allowed.
Here’s a list of pitchers who had perfect games through 8 2/3 innings. Here’s another list. It includes a 1917 game started by Babe Ruth of the Red Sox who walked the first batter and then was thrown out of the game. After he was replaced, the runner was thrown out trying to steal. Reliever Ernie Shore retired the next 26 batters.
Then there was today (4/13/22) when Clayton Kershaw was pulled after 7 perfect innings. I agree with Passan.