This chapter describes electromagnetic properties of 1D-and 2D-periodic arrays of metallic nanospheres that support plasmonic modes. Current fabrication possibilities are reported, and a simple formulation to analyze array electromagnetic properties is summarized. We review these properties, provide information about mode propagation in the array plane, and we analyze transmissivity, reflectivity and absorption when the array is illuminated by a plane wave, as well as the extinction cross section. Last, we summarize possible applications of arrays of plasmonic nanoparticles.