Parity (P) and time reversal (T) were once thought to be fundamental symmetries of nature; electromagnetism and gravity are "even" under these spacetime transformations. In the second half of the 20th century, experiments indicated that P and T are only approximate symmetries at low energies, yet the apparent absence of parity- and time-reversal-violating effects in the strong nuclear interactions poses one of the greatest theoretical problems with the Standard Model of particle physics. One dynamical solution to this puzzle involves a new particle---the QCD axion---which can also make up the dark matter of the universe. In this talk, I will describe two classes of experimental proposals designed to discover the QCD axion in the laboratory. They are based on a previously unknown phenomenon which we call the "piezoaxionic effect", akin to the piezoelectric effect typically present in parity-violating crystals. These phenomena and detectors are "odd" in the colloquial sense---they are unusual---but also in a precise sense: certain observables and material properties flip sign when viewed in a mirror (P-odd) or played backwards in time (T-odd).