Flow non-linearity is widespread in subsurface flow and affects transport in a variety of natural conditions and subsurface applications. Non-Newtonian fluids, whose viscosity depends on the local shear rate, are ubiquitous in such applications. Rheological complexity entails, in turn, solving non-linear mathematical problems that are far more challenging than those involving Newtonian fluids. Similar challenges are faced at the experimental level, where physico-chemical aspects, rheometry, visualization and imaging techniques become paramount. Another source of nonlinearity at the pore scale are inertial terms in the Navier-Stokes equations, whose effect at the Darcy scale is expressed by the Forchheimer law (among others). More generally, upscaling faces similar challenges when nonlinearity is compounded with the inherent multi-scale heterogeneity typical of porous or fractured media. We welcome contributions addressing the impact of flow non-linearity on transfers in subsurface media, based on theoretical/numerical studies, laboratory experiments, or macro-scale/field investigations, over a broad range of scales.