Transport phenomenon in porous media is of fundamental as well as practical importance in a wide spectrum of problems of different length and time scales, viz., enhanced oil recovery, carbon capture and storage, contaminant transport in subsurface aquifers, and chromatographic separation to name a few. These transport processes in porous media feature different hydrodynamic instabilities. Viscous fingers (VF) appear due to such an instability mechanism attributed to the mobility mismatch between the invading and defending fluids–a less mobile defending fluid allows the finger-like intrusion of a more mobile invading fluid. In this talk, we will discuss the interactions of VF with shock layer or rarefaction. Our approach is to combine two well-studied settings–VF dynamics in miscible fluids and shock layer (rarefaction) wavefronts–to investigate how these two nonlinear dynamics impact one another. Our analytical approach treats a solvent containing a finite slice of a solute that (a) is adsorbed on the porous matrix following a Langmuir adsorption isotherm and (b) influences the dynamic viscosity of the solution. A shock layer (rarefaction) wave generates at the frontal (rear) sample interface. VF formed at a viscously unstable rarefaction interface propagate through the finite sample to preempt the shock layer at the viscously stable front. However, no such event is observed when a shock layer front features VF. Implications for experiments and observations of chromatography separation will be discussed.