What plays can a manager challenge?

MLB lists these calls as reviewable:

• Potential home runs: whether the ball left the field, hit the top of a fence or a railing, was touched by a fan reaching over the fence, or was fair or foul.
• Non-home run boundary calls, such as a live ball bouncing out of play or a fielder catching a ball near a stadium boundary.
• Fair/foul calls, only on balls that first land at or beyond the set positions of the first- or third-base umpire.
• Force and tag plays, including whether the runner acquired the base.
• Outfield catches (fly balls or line drives in flight). Infield catches are not reviewable.
• Specified baserunning calls: passing a preceding runner, scoring ahead of a third out, and touching a base.
• Hit by pitch: whether the ball may have hit the player, his clothing or his bat. Whether the ball was in the strike zone and whether the batter tried to avoid it are not reviewable.
• Collisions at home plate, tag-ups, placement of runners after a boundary call, and interference on double plays.

Balls and strikes are not on the list.

Source: MLB, Replay Review (mlb.com/glossary/rules/replay-review).