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Magnetically tunable scattering resonances have been used with great successfor precise control of s-wave scattering lengths in ultracold atomiccollisions. We describe relatively simple yet quite powerful analytictreatments of such resonances based on the analytic properties of the van derWaals long range potential. This theory can be used to characterize a number ofproperties of specific resonances that have been used successfully in variousexperiments with $^{87}$Rb, $^{85}$Rb, $^{40}$K, and $^{6}$Li. Optical Feshbachresonances are also possible and may be practical with narrow intercombinationline photoassociative transitions in species like Sr and Yb.Comment: To be published in the Proceedings of the 20th International  Conference on Atomic Physics, held in Innsbruck, Austria, July 200

Simple Theoretical Models for Resonant Cold Atom Interactions