  This work reviews our current understanding of Cherenkov-type processes in
vacuum that may occur due to a possible violation of Lorentz invariance. The
description of Lorentz violation is based on the Standard Model Extension
(SME). To get an overview as general as possible, the most important findings
for vacuum Cherenkov radiation in Minkowski spacetime are discussed. After
doing so, special emphasis is put on gravitational Cherenkov radiation. For a
better understanding, the essential properties of the gravitational SME are
recalled in this context. The common grounds and differences of vacuum
Cherenkov radiation in Minkowski spacetime and in the gravity sector are
emphasized.
