CPT and Lorentz Invariance: Their Relation and Violation

The CPT theorem in quantum field theory, its validity, breaking and consequences are reviewed. One can show that for CPT theorem to hold, Lorentz invariance is not always needed. Also one can have CPT violation, while there is Lorentz invariance. Field theoretical examples for both cases are given and mass differences between particle-antiparticle are discussed as well. Unambiguous tests of CPT violation, unrelated to the breaking of Lorentz invariance, are suggested.