In most cases, the non-penalized team will have the option of declining the penalty; in which case the results of the previous play stand as if the penalty had not been called. One notable exception to this rule is if the kicking team on a 3rd down punt play is penalized before the kick occurs: the receiving team may not decline the penalty and take over on downs. After the kick is made, change of possession occurs and subsequent penalties are assessed against either the spot where the ball is caught, or the runback.
Who can decline a previous play?