Abstract The Josephson plasma wave emerging in layered HTSC is a very unique collective excitation which is assigned to a composite wave of the Josephson current and the electromagnetic field. Single crystals of layered HTSC correspond to multi-stacked Josephson junction arrays and the Josephson plasma oscillations are collectively excited over all junctions, that is, the crystals as a whole respond to AC electromagnetic perturbations. Experimentally, the Josephson plasma excitations have been observed by the optical reflectivity and the microwave resonant absorption. On the other hand, theoretically, the nature of the Josephson plasma waves and related electromagnetic behaviors can be studied using the equations for the superconducting phase. First, we point out that the measurements of the plasma resonance provide a useful tool to study the nature and stateof the vortices in HTSC since the Josephson plasma strongly interacts with the vortices. Second, we illustrate some related in intriguing electromagnetic behaviors including the interaction with the Josephson vortex, for example, a Cherenkov like radiation of the Josephson plasma. Finally, we suggest a way to excite the Josephson plasma effectively, that is, we show that a superradiation of the Josephson plasma is theoretically possible.