Parity violation leads to energy differences delta(pv)H(o)(0)=N(A)delta(pv)E of enantiomers in the femtojoule to picojoule per mole range. Recently introduced methods of electroweak quantum chemistry predict such energy differences to be one to two orders of magnitude larger than previously accepted-but still very small. How can such small energies be measured and what are the consequences for our understanding of molecular chirality, biomolecular homochirality, and perhaps fundamental physics? The review gives some tentative answers to these questions. We discuss the current status of theory and some of the current experimental approaches.