In this thesis, we investigate two issues of current interest in relativistic quantum mechanics. In the first one, we study the Dirac and Klein–Gordon equations with noncentral scalar and vector potentials of equal magnitudes. This is done as an attempt to give a proper physical interpretation of this class of problems in which interest has surged recently. The relativistic energy spectra are obtained and shown to differ from those of well-known problems that have the same non-relativistic limit. Consequently, such problems should not be misinterpreted as the relativistic extension of the given potentials. Additionally, we shed new light in some related issues in spin and pseudo-spin symmetry in nuclear physics. In the second topic, we derive a non-relativistic quantum mechanical equation for a system with spatially dependent mass with a unique removal of the ordering ambiguity. This is done by starting from the Dirac equation (with electromagnetic interaction) that does not suffer from this ambiguity and then taking the non-relativistic limit, which is unique. New terms in the Hamiltonian are found, some of which are given physical interpretation.