John Stewart Bell, a physicist born in Belfast and employed at CERN, published in 1964 the paper 'On the Einstein Podolsky Rosen Paradox', mathematically demonstrating that no local hidden-variable theory — the alternative Einstein, Podolsky, and Rosen had proposed in 1935 to avoid the 'spooky action at a distance' of quantum entanglement — can reproduce all the predictions of quantum mechanics. Bell formulates a concrete statistical inequality: if the universe is local and deterministic in the classical sense, the correlations between entangled particles cannot exceed a certain limit. Quantum mechanics predicts that they do exceed it. The theorem converts a three-decade-old philosophical debate into a testable experimental question. John Clauser performs the first experimental verification in 1972; Alain Aspect closes the main experimental loopholes in 1981-82 at Orsay; Anton Zeilinger extends the verifications in the 1990s and develops quantum teleportation techniques. The violations of Bell's inequalities, confirmed in every experiment, establish that quantum entanglement is real and cannot be reproduced by classical hidden variables. It is the experimental foundation of quantum cryptography, quantum computing, and quantum information teleportation.