One-dimensional propagation of transient electromagnetic waves in periodic media is studied. The media are periodic in the direction of propagation and can be of finite or infinite length. Wave propagators that map a transient field from one point in the medium to another are introduced. A number of useful relations for the propagators are presented. Some of these relations are used in the determination of explicit expressions for the short time behavior of a transient wave as it propagates in a periodic medium. The theory is exemplified by several numerical examples.