The accurate description of molecular diffusion is important in the design and development of several processes of interest to chemical engineers. Most commonly, a component diffuses down the gradient of its concentration, and Fick's law provides an adequate description for calculation of the fluxes. The major objective of this review article is to highlight a wide variety of processes in which a component is transported uphill, requiring more rigorous models for describing diffusion. Uphill diffusion may occur in multicomponent mixtures in which the diffusion flux of any species is strongly coupled to that of partner species. Such coupling effects often arise from strong thermodynamic non-idealities; for a quantitative description we need to use the Maxwell-Stefan formulation with chemical potential gradients as driving forces. Thermodynamic non-idealities are of particular significance for operations close to phase transition regions. A careful and detailed analysis of multicomponent distillation, and extraction processes reveals that Murphree component efficiencies could be "unbounded", i.e. exhibit values less than zero or exceed unity. A characteristic signature of uphill diffusion is the occurrence of transient overshoots in the approach to steady-state; the equilibration trajectories in composition space follow serpentine trajectories. For mixtures of liquids, metals, alloys, ceramics and glasses the serpentine equilibration trajectories could cause forays into meta-stable composition zones; such forays could result in spontaneous emulsification, and the Ouzo effect. The transport of ionic species is invariably coupled with its partner ions because of the electroneutrality constraints; such constraints may accelerate or decelerate a specific ion resulting in uphill transport. The forward and reverse kinetics of uptake in ion-exchange resins are asymmetric. For mixture separations with microporous adsorbents, uphill diffusion can cause supra-equilibrium loadings to be achieved during transient uptake within crystals; this allows the possibility of overriding adsorption equilibrium for achieving difficult separations. (C) 2018 Elsevier Ltd. All rights reserved.