The history of models of elementary-particle interactions in a spacetime with large extra dimensions is reviewed, and the current state of this approach and its phenomenological implications are considered. The discussion is focused on the stabilized two-brane Randall—Sundrum model — the most interesting one from this perspective — and the most important results it yields. For this model, the connection between the fundamental 5D energy scale and the Planck mass is discussed in detail, as is the isolation of physical degrees of freedom. The interaction of the lowest scalar mode, the radion, and the lowest tensor modes with Standard Model fields is analyzed. The stability of the model with respect to quantum corrections is discussed.