  Given any smooth, suitably small initial data, which decays polynomially at
infinity, we prove global regularity for the $3D$ relativistic massive
Vlasov-Maxwell system. In particular, the compact support assumption, which is
widely used in the literature, is not imposed on the initial data. Our proofs
are based on a combination of the Klainerman vector fields method and the
Fourier method, which allows us to exploit a crucial hidden null structure in
the relativistic Vlasov-Maxwell system.
