This paper proposes a general characterization of one dimensional multiple periodic (MP) structures for electromagnetic transmission and radiation. Studies are conducted from three aspects: Firstly, the dispersion relations of non-dispersive (conventional) and dispersive (composite right/left-handed (CRLH)) materials are analyzed. Regarding each category of materials, detailed analyses for distributed layered media and lumped circuits are presented. Through studies, we found that the periodicity increase opens up multiple stopbands. According to our physical explanations and numerical results, the relation between stopbands and periodicity is clarified. Additionally, the periodicity increase also reduces the separation distance of space harmonic modes along the phase constant axis in the dispersion diagram. Thus, more space harmonic modes are excited in the radiation. This phenomenon results in simultaneous right- and left-handed radiation and multiple radiation beams. Secondly, mathematical formulas for the general dispersion relation and the general Bragg condition of the MP structures are derived. The formulas help to indicate the locations of stopbands and engineer the dispersion relation. Thirdly, applications of the MP structures to phase reversal (PR) antennas are presented. Both transmission and radiation characteristics of the MP structures are validated by the PR antennas experimentally. Single, double and triple periodic structures are comparatively studied.