  Magnetically tunable scattering resonances have been used with great success
for precise control of s-wave scattering lengths in ultracold atomic
collisions. We describe relatively simple yet quite powerful analytic
treatments of such resonances based on the analytic properties of the van der
Waals long range potential. This theory can be used to characterize a number of
properties of specific resonances that have been used successfully in various
experiments with $^{87}$Rb, $^{85}$Rb, $^{40}$K, and $^{6}$Li. Optical Feshbach
resonances are also possible and may be practical with narrow intercombination
line photoassociative transitions in species like Sr and Yb.
