The use of microwave radiation to drive chemical reactions has become ubiquitous in almost all fields of chemistry. In all of these areas it is principally due to rapid and convenient heating resulting in significantly higher rates of reaction, with other advantages including enhanced product selectivity and control of materials properties. Although microwave heating continues to grow as an enabling technology, fundamental research into the nature of microwave heating has not grown at the same rate. In the case of chemical reactions run in homogeneous solution, particularly synthetic organic reactions, there is considerable controversy over the origins of rate enhancement, with a fundamental question being whether there exist microwave-specific effects, distinct from what can be attained under conventional convective heating, that can accelerate a reaction rate. In this Perspective, we discuss unique aspects of microwave heating of molecules in solution and discuss the origin and nature of microwave-specific effects arising from the process of "selective heating" of reactants in solution. Integral to this discussion is work from the field of dielectric relaxation spectroscopy, which provides a model for selective heating by Debye relaxation processes. The Perspective also includes a critical discussion of hypotheses of non-thermal effects (alternatively classified here as resonant processes) and an outline of specific reaction parameters for chemical systems in which microwave-specific Debye relaxation processes can result in observable reaction rate enhancement.