The classical theory of dispersive signal propagation by Sommerfeld and Brillouin proposed in 1914 provided the first proof within the classical Maxwell–Lorentz theory that an electromagnetic signal could not propagate faster than the vacuum speed of light in a causal dielectric, also introducing the signal velocity and the precursor fields (or forerunners). Modern asymptotic theory has extended these results, providing a physically meaningful definition of the signal velocity while showing the critical role that the precursor fields play in the observed pulse dynamics. Their role in defining the observed pulse velocity is presented and compared with the classical group velocity as well as with other pulse velocity measures that yield superluminal results.