In this lecture, Alain Aspect will first explain Einstein's reasoning about entangled particles. That reasoning led to his conclusion that quantum mechanics is not complete, in contradiction with Bohr's point of view. Aspect will then show how Bell's inequalities have allowed experimentalists to settle the debate, emphasizing the most extraordinary features of entanglement and prompting the emergence of basic ideas for quantum information and quantum communication. These ideas are enabling the development of new technologies in many academic and industrial laboratories.