  Time-Reversal-Invariance non-conservation has for the first time been
unequivocally demonstrated in a direct measurement, one of the results of the
CPLEAR experiment. What is the situation then with regard to
time-reversal-invariance non-conservation in systems other than the neutral
kaon system? Two classes of tests of time-reversal-invariance need to be
distinguished: the first one deals with parity violating
(P-odd)/time-reversal-invariance non-conserving (T-odd) interactions, while the
second one deals with P-even/T-odd interactions (assuming CPT conservation this
implies C-conjugation non-conservation). Limits on a P-odd/T-odd interaction
follow from measurements of the electric dipole moment of the neutron. This in
turn provides a limit on a P-odd/T-odd pion-nucleon coupling constant which is
10^-4 times the weak interaction strength. Limits on a P-even/T-odd interaction
are much less stringent. The better constraint stems also from the measurement
of the electric dipole moment of the neutron. Of all the other tests,
measurements of charge-symmetry breaking in neutron-proton elastic scattering
provide the next better constraint. The latter experiments were performed at
TRIUMF (at 477 and 347 MeV) and at IUCF (at 183 MeV). Weak decay experiments
(the transverse polarization of the muon in K+ -> pi0 mu+ nu and the transverse
polarization of the positrons in polarized muon decay) have the potential to
provide comparable or possibly better constraints.
