Many practical systems in physics, biology, engineering, and information science exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynamical processes. This paper introduces the impulsive behavior into switched linear systems and studies the reachability and controllability of such systems. Necessary and sufficient criteria for reachability and controllability are established. It is proved that reachability is equivalent to controllability for such systems. Our criteria are of geometric type, they can be transformed into algebraic type conveniently.