Abstract: Symmetries and their Breaking play a crucial role in the Fundamental Laws of Physics. Interactions as well as particle content are dictated by the requirement of imposing symmetry - or asymmetry in a definite way -. The Discrete Symmetries of Parity P, Charge-Conjugation C, CP, Time Reversal T and CPT are guiding principles in the behaviour of nature. Their present status and studies will be summarized.

The system of neutral K and B mesons is of particular interest for the studies of CP, T and CPT. For the antiunitary symmetries T and CPT, the irreversibility of the decay was considered to be a NO-GO argument for their study in transitions. I shall discuss the BYPASS, using Entanglement and the Decay as a Filtering Projection, able to construct Direct, Genuine and Separate Asymmetries to be measured in the B and PHI Factories. Time-Reversal-Violation has been observed by BABAR for B's using this conceptual basis, and the analysis is being completed by KLOE-2 for K's.

The limits and prospects of CPT-Asymmetries in different meson transitions will be presented.