I will discuss the phenomenon of emergent Lorentz invariance in strongly coupled theories. Lorentz Invariance is imprinted by the renormalization group flow in most observables, such as the dispersion relations of composite particles at low energies. Thanks to the strong dynamics, the deviations from the relativistic form at low energies are power-law suppressed by the ratio of the compositeness and the microscopic scales. This allows to pass the tests on violations of Lorentz invariance without fine-tuning. I will comment on the implications for particle physics and condensed matter.