The ability of turbulent flows to effectively mix entrained fluids to a molecular scale is a vital part of the dynamics Of Such flows, with wide-ranging consequences in nature and engineering. It is a considerable experimental, theoretical, modeling, and computational challenge to capture and represent turbulent mixing which, for high Reynolds number (Re) flows, occurs across a spectrum of scales of considerable span. This consideration alone places high-Re mixing phenomena beyond the reach of direct simulation, especially in high Schmidt number fluids, such as water, in which species diffusion scales are one and a half orders of magnitude smaller than the smallest flow scales. The discussion below attempts to provide an overview of turbulent mixing; the attendant experimental, theoretical, and computational challenges; and suggests possible future directions for progress in this important field.