We revisit the theory of Cherenkov radiation in uniaxial crystals. Historically, a number of flawed attempts have been made at explaining this radiation phenomenon, and a consistent error-free description is nowhere available. We apply our calculation to a large modern day telescope - IceCube. Located in Antarctica, this detector makes use of the naturally occurring ice as a medium to generate Cherenkov radiation. However, due to the high pressure at the depth of the detector site, large volumes of hexagonal ice crystals are formed. We calculate how this affects the Cherenkov radiation yield and angular dependence. We conclude that the effect is small, at most about a percent, and would only be relevant in future high-precision instruments like e.g. Precision IceCube Next Generation Upgrade (PINGU). For radio-Cherenkov experiments which use the presence of a clear Cherenkov cone to determine the arrival direction, any variation in emission angle will directly and linearly translate into a change in apparent neutrino direction. In closing, we also describe a simple experiment to test this formalism and calculate the impact of anisotropy on light yields from lead tungstate crystals as used, for example, in the CMS calorimeter at the CERN LHC.