  The review covers transitions between M0 and M0bar in all four systems M0 =
K0, D0, B0 and Bs. These systems are ideal laboratories for studying the
discrete symmetries T and CPT. The properties of time reversal T are discussed
in classical and quantum mechanics. T violation in K0 K0bar transitions has
been observed in 1970 independent of assuming CPT symmetry by using the
Bell-steinberger unitarity relation. Improvements of this observation are
reviewed including the latest results in 2013. They show with high significance
that CP violation in K0 K0bar transitions is only T violation without any CPT
violation. Transitions in the other three systems do not show CP violation so
far and therefore neither T nor CPT violation. The large observed CP violation
in B0 -> J/psi K0 decays is presented to be compatible with only T and no CPT
violation, the same for the very small but significant CP violation in decays
K0 -> pi pi with isospin 2.
