This colloquium analyzes the interaction of light with two-dimensional periodic arrays of particles and holes. The enhanced optical transmission observed in the latter and the presence of surface modes in patterned metal surfaces are thoroughly discussed. A review of the most significant discoveries in this area is presented first. A simple tutorial model is then formulated to capture the essential physics involved in these phenomena, while allowing analytical derivations that provide deeper insight. Comparison with more elaborated calculations is offered as well. Finally, hole arrays in plasmon-supporting metals are compared to perforated perfect conductors, thus assessing the role of plasmons in these types of structures through analytical considerations.