Rules side by side
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A coach in the NFL gets two. A manager in baseball gets one, or two if the first succeeds. The differences are in what can be reviewed.

All four leagues allow coaches to ask for a play to be reviewed on video, but the rules on how often and what is eligible vary by sport.
NFL
Each head coach has two challenges a game, and a third is granted if both of the first two succeed. A failed challenge costs a timeout. Scoring plays and turnovers are reviewed automatically by the replay official, and in the last two minutes of each half all reviews are initiated by the booth, not the coach.
MLB
A manager starts each game with one challenge. If the call is overturned, he keeps it and gets a second. From the seventh inning, the umpire crew chief can also order a review without a challenge. Strike calls and balls are not reviewable.
NBA
Each team has one coach's challenge per game, available since the 2019–20 season, and it can be used on a personal foul, a goaltending call or an out-of-bounds decision. A successful challenge preserves the timeout; an unsuccessful one costs it. Other reviews, such as shot-clock and flagrant-foul checks, are started by the officials themselves.
NHL
The NHL has a coach's challenge for goaltender interference and offside plays that lead to a goal. A failed challenge carries a cost, which under the league's rules has been the loss of a timeout or a minor penalty for delay of game, so a team weighs the risk before using it.
What these have in common
In each league the number is small and a wrong challenge has a price, so a coach tends to save his challenge for the plays that decide a game.