A scrimmage kick in football is any kick that is performed by the special teams that happens on the line of scrimmage. Punts, field goals, and PATs are all scrimmage kicks. Scrimmage kicks are performed during particular game scenarios either after a touchdown or if a team is giving the other team possession of the ball.
When a scrimmage kick crosses into the neutral zone, it cannot be touched. However, if it doesn't cross the neutral zone, it can be played, passed or even kicked again by another player.
Scrimmage kicks must be performed on a scrimmage down in order for it to be considered legal, by a member of the team that snapped the ball. A punt is a scrimmage kick that is performed to change possession of the ball. This occurs when a player drops the ball in front of him and kicks it high and far before it hits the ground.
Field goals are taken by a special teams player if there is limited time left in the quarter and only enough time for one more play. Field goal kicks are also taken on the line of scrimmage if it is the 4th down and the chances of scoring the field goal are high.