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This paper aims to provide a review and critical analysis of the state of the art concerning crowd-structure interaction phenomena on footbridges. The problem of lateral vibrations induced by synchronised pedestrians, namely the Synchronous Lateral Excitation, is specifically addressed. Due to the multi-physic and multi-scale nature of the complex phenomenon, several research fields can contribute to its study, from structural engineering to biomechanics, from transportation engineering to physics and applied mathematics. The different components of the overall coupled dynamical system - the structure, the crowd and their interactions - are separately analysed from both a phenomenological and modelling point of view. A special attention is devoted to those models, which explicitly account for the interaction between mechanical and living systems.