Nonequilibrium mesoscopic transport: a genealogy

Models of nonequilibrium quantum transport underpin all modern electronic devices, from the largest scales to the smallest. Past simplifications such as coarse graining and bulk self-averaging served well to understand electronic materials. Such particular notions become inapplicable at mesoscopic dimensions, edging towards the truly quantum regime. Nevertheless a unifying thread continues to run through transport physics, animating the design of small-scale electronic technology: microscopic conservation and nonequilibrium dissipation. These fundamentals are inherent in quantum transport and gain even greater and more explicit experimental meaning in the passage to atomic-sized devices. We review their genesis, their theoretical context, and their governing role in the electronic response of meso- and nanoscopic systems. (topical review)