This colloquium by F. J. García de Abajo discusses the interaction of light with two-dimensional periodic arrays of particles and holes, focusing on enhanced optical transmission in hole arrays and the presence of surface modes in patterned metal surfaces. The author reviews significant discoveries in this area, formulates a simple tutorial model to capture the essential physics, and compares it with more detailed calculations. The tutorial model is based on analytical relations for the scattering of an external light plane wave on a periodic array of small particles or holes, allowing for the derivation of simple expressions that provide deeper insights into the phenomena. The model is applied to both single holes and particle arrays, and the interplay between lattice and site resonances is explored. The author also compares hole arrays in plasmon-supporting metals with perforated perfect conductors, assessing the role of plasmons in these structures through analytical considerations. The colloquium highlights the importance of these phenomena in various applications, including frequency-selective filters, biosensing, and all-optical switching.This colloquium by F. J. García de Abajo discusses the interaction of light with two-dimensional periodic arrays of particles and holes, focusing on enhanced optical transmission in hole arrays and the presence of surface modes in patterned metal surfaces. The author reviews significant discoveries in this area, formulates a simple tutorial model to capture the essential physics, and compares it with more detailed calculations. The tutorial model is based on analytical relations for the scattering of an external light plane wave on a periodic array of small particles or holes, allowing for the derivation of simple expressions that provide deeper insights into the phenomena. The model is applied to both single holes and particle arrays, and the interplay between lattice and site resonances is explored. The author also compares hole arrays in plasmon-supporting metals with perforated perfect conductors, assessing the role of plasmons in these structures through analytical considerations. The colloquium highlights the importance of these phenomena in various applications, including frequency-selective filters, biosensing, and all-optical switching.