A review is presented of light-intensity interference experiments demonstrating the inadequacy of the classical concept of a priori properties of quantum objects (Bell's theorem). A detailed description of experimental procedures using N-photon light (N = 2,3,...) is given and is accompanied by interpretations of experimental data in terms of quantum theory and a variety of clear classical models. Different formulations of the conflict between classical ideas and quantum theory are presented, including the Bell theorem without inequalities, the Kochen–Specker theorem, and so on.