  The use of operator methods of algebraic nature is shown to be a very
powerful tool to deal with different forms of relativistic wave equations. The
methods provide either exact or approximate solutions for various forms of
differential equations, such as relativistic Schr\"odinger, Klein-Gordon and
Dirac. We discuss the free particle hypotheses and those relevant to particles
subject to non-trivial potentials. In the latter case we will show how the
proposed method leads to easily implementable numerical algorithms.
