The discovery of the Meissner (Meissner–Ochsenfeld) effect in 1933 was an incontestable turning point in the history of superconductivity. First, it demonstrated that superconductivity is an unknown before equilibrium state of matter, thus allowing to use the power of thermodynamics for its study. This provided a justification for the two-fluid model of Gorter and Casimir, a seminal thermodynamic theory founded on a postulate of zero entropy of the superconducting (S) component of conduction electrons. Second, the Meissner effect demonstrated that, apart from zero electric resistivity, the S phase is also characterized by zero magnetic induction. The latter property is used as a basic postulate in the theory of F. and H. London, which underlies the understanding of electromagnetic properties of superconductors. Here the experimental and theoretical aspects of the Meissner effect are reviewed. The reader will see that, in spite of almost nine decades age, the London theory still contains questions, the answers to which can lead to a revision of the standard picture of the Meissner state (MS) and, if so, of other equilibrium superconducting states. An attempt is made to take a fresh look at electrodynamics of the MS and try to work out with the issues associated with the description of this most important state of all superconductors. It is shown that the concept of Cooper’s pairing along with the Bohr–Sommerfeld quantization condition allows one to construct a semi-classical theoretical model consistently addressing properties of the MS and beyond, including non-equilibrium properties of superconductors caused by the total current. As follows from the model, the three “big zeros” of superconductivity (zero resistance, zero induction and zero entropy) have equal weight and grow from a single root: quantization of the angular momentum of paired electrons. The model predicts some yet unknown effects. If confirmed, they can help in studies of microscopic properties of all superconductors. Preliminary experimental results suggesting the need to revise the standard picture of the MS are presented.