What happens to runs scored after a decision is overturned on review?

Out changed to Not out: the ball is still treated as dead from the moment the original Out decision was made. The batting side gets the batter back but no runs that might have followed if the umpire had said Not out, except any No ball penalty found during your checks.

Not out changed to Out: the ball is treated as dead from the moment of the dismissal. Everything after that, including any runs, is ignored.

No ball found after a dismissal (on an umpire's check): the batting side gets the dismissal reversed and the one-run No ball penalty, but no runs that might have followed had No ball been called at the time. If the batters crossed while a catch was in the air, they go back to their original ends as if the striker had been out, and the striker isn't credited with any runs completed before the catch. Obstructing the field is the exception: a batter can still be out that way off a No ball.

If the mode of dismissal isn't obvious, or differs from the original decision, the on-field umpire tells the scorers through you.