The polarization of light admits elegant geometric descriptions both in the paraxial and nonparaxial regimes. For paraxial fields, the state of polarization can be represented as a point over what is known as the Poincaré sphere, which is an abstract spherical parameter space. We will discuss how certain fields can cover all polarization states according to certain topological rules, so that they can be considered as optical “skyrmions”, in analogy with the topological spin textures of the same name.