We examine analytically and numerically the evolution of a relativistic fireball. We show that, after an early rearrangement phase, most of the matter and energy in the fireball is concentrated within a narrow shell. The shell propagates at nearly the speed of light, with a frozen radial profile and according to a simple set of scaling laws. The spectrum of the escaping radiation is harder at early times and softer later on. The results are applicable to models of $\gamma$-ray bursts. Submitted to Monthly Notices of the RAS Figures available on request from the authors