The interplay between forces generated by rigid bodies moving through fluids can be significantly affected by the presence of density variations in the fluid. This talk will present a theoretical and experimental study of what can be viewed as one of the simplest set-ups where density effects in this context can be analyzed. We consider spheres falling under gravity through miscible, sharply stratified fluids under viscosity-dominated (Stokes) dynamics. A first-principles, numerically-assisted mathematical model of this system will be presented. Analysis of our theory identifies parametric trends,  which are also partially explored in the experiments, further confirming the predictive capability of the theoretical model. Even for such simple systems, some new, and perhaps non-intuitive, physical phenomena emerge, as illustrated by the example of two identical spheres racing to the bottom of homogeneous vs. stratified fluids. Conversely, some non-physical properties of Stokes flows in the limit of large domains can be resolved by stratification. An example of how stratification may modify the Stokes (or Whitehead) paradox will be discussed, together with some mathematical implications for the analysis of the motion equations in exterior domains.