This colloquium explores the interaction of light with two-dimensional periodic arrays of particles and holes. It discusses enhanced optical transmission in hole arrays and surface modes in patterned metal surfaces. The review highlights key discoveries in this field, presenting a simple model to understand the essential physics, allowing analytical derivations. The model is compared with more complex calculations, and hole arrays in plasmon-supporting metals are compared to perforated perfect conductors to assess the role of plasmons. The scattering of waves in periodic media is central to various areas of physics, including electron diffraction and atomic-beam scattering. Light in photonic crystals undergoes diffraction that can limit propagation in band gaps. The ratio of the period to the wavelength determines the regime of interest, with different behaviors observed in the limits of λ >> a, λ << a, and λ ~ a. The colloquium begins with an introduction to the topic, followed by an overview of existing results. It discusses single holes, optical transmission through hole arrays, and particles. A tutorial approach is then presented, formulating a simple model to capture the physics of these phenomena. The model is used to derive analytical expressions and is compared with more elaborate calculations. The role of plasmons in metals is discussed, comparing them to perfect conductors. Key findings include the enhanced optical transmission through hole arrays, which can be several times larger than predictions for non-interacting holes. The transmission is influenced by factors such as hole shape, size, and the dielectric environment. The phenomenon is linked to Wood's anomalies and the Rayleigh condition. The transmission is also affected by the interaction between holes and surface plasmons, as well as dynamical light diffraction. The colloquium also discusses lattice surface modes in structured metals, the interplay between lattice and site resonances, and the behavior of slit and cylinder arrays. It concludes with a summary of the main findings, emphasizing the importance of these phenomena in understanding light scattering by periodic structures. The results are supported by experimental and theoretical studies, highlighting the significance of these effects in various applications.This colloquium explores the interaction of light with two-dimensional periodic arrays of particles and holes. It discusses enhanced optical transmission in hole arrays and surface modes in patterned metal surfaces. The review highlights key discoveries in this field, presenting a simple model to understand the essential physics, allowing analytical derivations. The model is compared with more complex calculations, and hole arrays in plasmon-supporting metals are compared to perforated perfect conductors to assess the role of plasmons. The scattering of waves in periodic media is central to various areas of physics, including electron diffraction and atomic-beam scattering. Light in photonic crystals undergoes diffraction that can limit propagation in band gaps. The ratio of the period to the wavelength determines the regime of interest, with different behaviors observed in the limits of λ >> a, λ << a, and λ ~ a. The colloquium begins with an introduction to the topic, followed by an overview of existing results. It discusses single holes, optical transmission through hole arrays, and particles. A tutorial approach is then presented, formulating a simple model to capture the physics of these phenomena. The model is used to derive analytical expressions and is compared with more elaborate calculations. The role of plasmons in metals is discussed, comparing them to perfect conductors. Key findings include the enhanced optical transmission through hole arrays, which can be several times larger than predictions for non-interacting holes. The transmission is influenced by factors such as hole shape, size, and the dielectric environment. The phenomenon is linked to Wood's anomalies and the Rayleigh condition. The transmission is also affected by the interaction between holes and surface plasmons, as well as dynamical light diffraction. The colloquium also discusses lattice surface modes in structured metals, the interplay between lattice and site resonances, and the behavior of slit and cylinder arrays. It concludes with a summary of the main findings, emphasizing the importance of these phenomena in understanding light scattering by periodic structures. The results are supported by experimental and theoretical studies, highlighting the significance of these effects in various applications.