The review presents the history of models of interactions of elementary particles in spacetime with large extra dimensions, discusses the current state of this approach and its phenomenological consequences. The main attention is paid to the stabilized Randall—Sundrum model with two branes, which is the most interesting from this point of view, and the most important results obtained within it. For this model, the connection of the fundamental five-dimensional energy scale with the Planck mass and the identification of physical degrees of freedom are discussed in detail. The interaction of the lowest scalar mode, the radion, and the lowest tensor modes with the fields of the Standard Model is considered. The stability of the model with respect to quantum corrections is discussed.