Historically, a great deal of attention has been addressed to the question of what it would take to test experimentally the metrical structure of spacetime. Arguably, however, consideration of this question has been at the expense of comparable investigations into what it would take to test other structural features of spacetime. In this article, we critique and expand substantially upon an article by Hadley (Hadley in Class Quantum Gravity, 19:4565–4571, 2002), which constitutes one of the best-known paper-length studies of what (...) it would take to test the orientability of spacetime. In so doing, we seek to clarify a number of matters which remain unclear in the wake of Hadley’s article, thereby allowing the literature on this topic to progress. More positively, we also present, compare, and evaluate a number of other potential approaches to testing the orientability of spacetime which have arisen in the recent physics literature. (shrink)