Dielectric anisotropy in ice alters the propagation of polarized radio waves, so polarimetric radar sounding can be used to survey anisotropic properties of ice masses. Ice anisotropy is either intrinsic, associated with ice‐crystal orientation fabric (COF), or extrinsic, associated with material heterogeneity, such as bubbles, fractures, and directional roughness at the glacier bed. Anisotropy develops through a history of snow deposition and ice flow, and the consequent mechanical properties of anisotropy then feed back to influence ice flow. Constraints on anisotropy are therefore important for understanding ice dynamics, ice‐sheet history, and future projections of ice flow and associated sea‐level change. Radar techniques, applied using ground‐based, airborne, or spaceborne instruments, can be deployed more quickly and over a larger area than either direct sampling, via ice‐core drilling, or analogous seismic techniques. Here, we review the physical nature of dielectric anisotropy in glacier ice, the general theory for radio‐wave propagation through anisotropic media, polarimetric radar instruments and survey strategies, and the extent of applications in glacier settings. We close by discussing future directions, such as polarimetric interpretations outside COF, planetary and astrophysical applications, innovative survey geometries, and polarimetric profiling. We argue that the recent proliferation in polarimetric subsurface sounding radar marks a critical inflection, since there are now several approaches for data collection and processing. This review aims to guide the expanding polarimetric user base to appropriate techniques so they can address new and existing challenges in glaciology, such as constraining ice viscosity, a critical control on ice flow and future sea‐level change.