  Bell's inequality sets a strict threshold for how strongly correlated the
outcomes of measurements on two or more particles can be, if the outcomes of
each measurement are independent of actions undertaken at arbitrarily distant
locations. Quantum mechanics, on the other hand, predicts that measurements on
particles in entangled states can be more strongly correlated than Bell's
inequality would allow. Whereas experimental tests conducted over the past
half-century have consistently measured violations of Bell's
inequality---consistent with the predictions of quantum mechanics---the
experiments have been subject to one or more "loopholes," by means of which
certain alternatives to quantum theory could remain consistent with the
experimental results. This chapter reviews three of the most significant
loopholes, often dubbed the "locality," "fair-sampling," and
"freedom-of-choice" loopholes, and describes how recent experiments have
addressed them.
