In this paper, we revise the main features of pseudospin and spin symmetries of the Dirac equation with scalar and vector potentials and mention several of its applications to strong interacting physical systems. We present some recent results in which these symmetries are applied to Coulomb potentials in the Dirac equation in 1+1 dimensions, including also pseudoscalar potentials. These potentials are linear in |x| and may be applied in confining quark models. We explore all possible bound solutions, both for fermions and antifermions, and show the relation between spin and pseudospin symmetries by means of charge-conjugation and γ5 chiral transformations.