  The wave function of a composite system is defined in relativity on a
space-time surface. In the explicitly covariant light-front dynamics, reviewed
in the present article, the wave functions are defined on the plane $\omega \cd
x=0$, where $\omega$ is an arbitrary four-vector with $\omega^2=0$. The
standard non-covariant approach is recovered as a particular case for $\omega =
(1,0,0,-1)$. Using the light-front plane is of crucial importance, while the
explicit covariance gives strong advantages emphasized through all the review.
  The properties of the relativistic few-body wave functions are discussed in
detail and are illustrated by examples in a solvable model. The
three-dimensional graph technique for the calculation of amplitudes in the
covariant light-front perturbation theory is presented.
  The structure of the electromagnetic amplitudes is studied. We investigate
the ambiguities which arise in any approximate light-front calculations, and
which lead to a non-physical dependence of the electromagnetic amplitude on the
orientation of the light-front plane. The elastic and transition form factors
free from these ambiguities are found for spin 0, 1/2 and 1 systems.
  The formalism is applied to the calculation of the relativistic wave
functions of two-nucleon systems (deuteron, scattering state), with particular
attention to the role of their new components in the deuteron elastic and
electrodisintegration form factors and to their connection with meson exchange
currents. Straigthforward applications to the pion and nucleon form factors and
the $\rho-\pi$ transition are also made.
