Quasi-exactly solvable relativistic soft-core Coulomb models

► The relativistic bound-state solutions of the soft-core Coulomb models. ► Quasi-exact treatments of the Dirac and Klein-Gordon equations for the soft-core Coulomb models. ► Solutions obtained in terms of the roots to the Bethe ansatz equations. ► The hidden Lie algebraic structure discussed for the models. ► Results useful in describing mesonic atoms and interaction of intense laser fields with atom.