Theoretical topics in spacetime-symmetry violations

The Lorentz- and CPT-violating Chern-Simons extension of electrodynamics is considered. In the context of N=4 supergravity in four spacetime dimensions, it is argued that cosmological solutions can generate this extension. Within Chern-Simons electrodynamics, theoretical and phenomenological topics are reviewed that concern the number of the remaining spacetime symmetries and the vacuum Cherenkov effect, respectively.