In this chapterwe present thefirst results on global attraction tosolitons forthe scalar wave field and the Maxwell field coupled to the charged relativistic particlewith density of charge satisfying the Wiener condition. In particular, the radiation damping in classical electrodynamics is rigorously proved for the first time (in this chapter, for the translation-invariant case). The proofs rely on calculation of energy radiation to infinity and canonical transformation to the comoving frame and use energy bound from below and the Wiener Tauberian theorem.