  The growth of interfacial instabilities during fluid displacements can be
driven by gradients in pressure, viscosity and surface tension, and by applying
external fields. Since displacements of non-Newtonian fluids such as polymer
solutions, colloidal and granular slurries are ubiquitous in natural and
industrial processes, understanding the growth mechanisms and fully-developed
morphologies of interfacial patterns involving non-Newtonian fluids is
extremely important. In this perspective, we focus on {displacement
experiments} wherein competition{s} between capillary, viscous, elastic and
frictional forces drive the onset and growth of interfacial instabilities in
confined geometries. We conclude by highlighting several exciting open problems
in this research area.
