  The purpose of this paper is twofold. In the first part, we provide a new
proof of the global existence of the solutions to the Vlasov-Maxwell system
with a small initial distribution function. Our approach relies on vector field
methods, together with the Glassey-Strauss decomposition of the electromagnetic
field, and does not require any support restriction on the initial data or
smallness assumption on the Maxwell field. Contrary to previous works on Vlasov
systems in dimension $3$, we do not modify the linear commutators and avoid
then many technical difficulties.
  In the second part of this paper, we prove a modified scattering result for
these solutions. More precisely, we obtain that the electromagnetic field has a
radiation field along future null infinity and approaches, for large time, a
smooth solution to the vacuum Maxwell equations. As for the Vlasov-Poisson
system, in constrast, the distribution function converges to a new density
function along modifications of the characteristics of the free relativistic
transport equation. In order to define these logarithmic corrections, we
identify an effective asymptotic Lorentz force. By considering logarithmical
modifications of the linear commutators, defined in terms of derivatives of the
asymptotic Lorentz force, we finally prove higher order regularity results for
the limit distribution function.
