This paper reviews the constraints that can be placed on the shapes of disk galaxies' dark halos using the distribution and kinematics of atomic hydrogen. These data indicate that dark halos are close to axisymmetric, with their axes of symmetry co-aligned with their disk axes. They also appear to be oblate, with shortest-to-longest axis ratios displaying quite a broad range of values from ~0.2 to ~0.8. These results are consistent with the predicted shapes of halos in cold dark matter scenarios, but rule out some of the more exotic dark matter candidates. However, the total number of measurements is still depressingly small, and more data are required if halo shape is to become a powerful diagnostic for theories of galaxy formation and evolution. ; Comment: 8 pages, 3 figures, using sprocl.sty (included) and psfig.sty. Invited talk at "The Shapes of Galaxies and their Halos," Yale, May 2001. To be published by World Scientific