  While General Relativity ranks undoubtedly among the best physics theories
ever developed, it is also among those with the most striking implications. In
particular, General Relativity admits solutions which allow faster than light
motion and consequently time travel. Here we shall consider a "pre-emptive"
chronology protection mechanism that destabilises superluminal warp drives via
quantum matter back-reaction and hence forbids even the conceptual possibility
to use these solutions for building a time machine. This result will be
considered both in standard quantum field theory in curved spacetime as well as
in the case of a quantum field theory with Lorentz invariance breakdown at high
energies. Some lessons and future perspectives will be finally discuss.
