  Expository paper providing a historical survey of the gradual transformation
of the "philosophical discussions" between Bohr, Einstein and Schr\"odinger on
foundational issues in quantum mechanics into a quantitative prediction of a
new quantum effect, its experimental verification and its proposed (and loudly
advertised) applications. The basic idea of the 1935 paper of
Einstein-Podolsky-Rosen (EPR) was reformulated by David Bohm for a finite
dimensional spin system. This allowed John Bell to derive his inequalities that
separate the prediction of quantum entanglement from its possible classical
interpretation. We reproduce here their later (1971) version, reviewing on the
way the generalization (and mathematical derivation) of Heisenberg's
uncertainty relations (due to Weyl and Schr\"odinger) needed for the passage
from EPR to Bell. We also provide an improved derivation of the quantum
theoretic violation of Bell's inequalities. Soon after the experimental
confirmation of the quantum entanglement (culminating with the work of Alain
Aspect) it was Feynman who made public the idea of a quantum computer based on
the observed effect.
