Abstract: In this thesis I investigate the longevity of oscillons numerically, paying particular attention to spherically-symmetric oscillons that have been conjectured to have an infinitely-long lifetime.  In two spatial dimensions, oscillons have not been seen to decay.  In three spatial dimensions, specific initial Gaussian configurations seem to lead to oscillons with spikes in lifetime that have been conjectured to be infinite.  I discuss such “resonant” oscillons in two and three spatial dimensions, applying three tests to study their longevity: parametric resonance, virialization, and configurational entropy - an information theoretic measure of shape complexity.  Without offering a formal proof, the numerical results presented, within their precision, offer support for the conjecture that, in both dimensions, resonant oscillons may be infinitely long-lived.