I present the calculation of the EDM of the nucleon, deuteron, helion and triton induced by the QCDθ term, and by the minimal set of dimension-six parity and time-reversal violating operators. Using the tools of chiral EFT, I discuss how different symmetry properties of P and T violating operators at the quark-gluon level imply qualitatively different relations between observables in the one, two and three-nucleon sector. If experimentally observed, these relations would provide important clues to connect time-reversal violation in hadronic systems to its fundamental, microscopic source.