  We study the asymptotic properties of the small data solutions of the
Vlasov-Maxwell system in dimension three. No neutral hypothesis nor compact
support assumptions are made on the data. In particular, the initial decay in
the velocity variable is optimal. We use vector field methods to obtain sharp
pointwise decay estimates in null directions on the electromagnetic field and
its derivatives. For the Vlasov field and its derivatives, we obtain optimal
pointwise decay estimates by a vector field method where the commutators are
modification of those of the free relativistic transport equation. In order to
control high velocities and to deal with non integrable source terms, we make
fundamental use of the null structure of the system and of several hierarchies
in the commuted equations.
