This presentation will give an overview of several mathematical techniques that can be used for modeling optical fields, both in the paraxial and nonparaxial regimes. Two of these techniques, based respectively on "ray dressing" and generalizations of Wigner functions, exploit the simplicity of the ray model while rigorously incorporating wave effects like interference, coherence and polarization. Also discussed are new families of exact solutions of Maxwell's equations that are nonparaxial generalizations of Hermite- and Laguerre-Gaussian beams, as well as Airy beams. These fields constitute complete basis sets suitable for the modeling of strongly focused electromagnetic fields and their scattering off spherical objects. Finally, I will discuss the definition, generation, and applications of a family of paraxial beams which span all possible polarization states, as well as new, simple techniques for measuring coherence and polarization.