A new generation of experiments is being planned with a significant improvement in the sensitivity to electric dipole moments (EDMs) of the nucleon and light nuclei. Possible signals in these measurements would reflect time-reversal violation (TV) beyond that stemming from the phase of the CKM matrix. Could we then infer the origin of TV at the quark/gluon level? I describe our on-going program to relate nucleon and light-nuclear TV observables to various TV sources, such as the QCD theta term, quark EDMs, quark and gluon color-EDMs, etc. We use the effective field theory of QCD that is applicable to hadronic momenta of order of the pion mass - a generalization of chiral perturbation theory - and can handle one- and many-nucleon physics consistently. I argue that light nuclei could offer the key to disentangle TV sources.