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In this review, we highlight the physics of synchronization in collections of beating cilia and flagella. We survey the nonlinear dynamics of synchronization in collections of noisy oscillators. This framework is applied to flagellar synchronization by hydrodynamic interactions. The time-reversibility of hydrodynamics at low Reynolds numbers requires swimming strokes that break time-reversal symmetry to facilitate hydrodynamic synchronization. We discuss different physical mechanisms for flagellar synchronization, which break this symmetry in different ways
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