Recent advances in the development of implicit constitutive relations to describe the response of both solids and fluids have greatly increased the repertoire of the modeler in his ability to describe natural phenomena more faithfully than hitherto possible. It would not be an exaggeration to claim that such constitutive relations have the potential to lead to breakthroughs in mechanics as they provide very promising novel means to study two of the most important and ill-understood problems in mechanics, that of fracturing of solids and of turbulence in fluids, in addition to providing a means to describe a plethora of phenomena that have eluded explanation in biomechanics, response of colloids, and mixtures, etc. In this article, we describe these recent developments within the context of both fluid and solid mechanics.