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 ω·x = 0, where ω is an arbitrary four-vector with ω 2 = 0. The standard non-covariant approach is recovered as a particular case for ω = (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 lightfront 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 twonucleon 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 ρ − π transition are also made. ,0 = − 2η(F 1 − ηF 2 + G 1 /2) + η/2B 6 ,(6.63)The matrix elementsJ 11 ,J 1−1 have the same form as J 11 , J 1−1 , whereasJ 10 ,J 00 differ from J 10 , J 00 by the items containing the nonphysical form factors B 5 , B 6 , B 7 . Other nonphysical form factors B 1−4 and B 8 do not contribute to these matrix elements.The matrix elementsJ λ ′ λ do not satisfy the condition (6.61). SubstitutingJ λ ′ λ in eq.(6.61) instead of J λ ′ λ , we get: ∆ ≡ (1 + 2η)J 11 +J 1−1 − 2 2ηJ 10 −J 00 = −(B 5 + B 7 ) .(6.64)

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