  We explore the phenomenon of emergent Lorentz invariance in strongly coupled
theories. The strong dynamics is handled using the gauge/gravity
correspondence. We analyze how the renormalization group flow towards Lorentz
invariance is reflected in the two-point functions of local operators and in
the dispersion relations of the bound states. The deviations of these
observables from the relativistic form at low energies are found to be
power-law suppressed by the ratio of the infrared and ultraviolet scales. We
show that in a certain subclass of models the velocities of the light bound
states stay close to the emergent `speed of light' even at high energies. We
comment on the implications of our results for particle physics and condensed
matter.
