In this work, we investigate the hydrodynamic interactions between the curved boundaries in two contexts, (i) a compound particle in a background flow, (ii) an active particle near a curved wall. A droplet with an encapsulated particle is called a compound particle. We study the hydrodynamics of a compound particle in a linear flow. Analysis of the compound particle in different types of linear flows shows that strong hydrodynamic interaction between the encapsulated particle and the confining interface results in an increased deformation of the confining drop compared to that of a simple drop without an encapsulated particle. Our analysis also shows that the presence of an encapsulated particle always enhances the rheological quantities such as the effective shear viscosity, extensional viscosity, and normal stress differences in a dispersion of compound particles. In another context, we analyzed the effect of hydrodynamic interactions on the trajectory of an active particle (modelled as a squirmer) in the presence of a curved boundary. In this work, we compare and contrast the way in which the concave and convex curvatures affect the microswimmer dynamics and relate the observations to that of a flat wall. We show that irrespective of squirmer type and its strength, microswimmer has a greater affinity towards the concave curvature compared to the convex curvature. In the absence of steric interactions, we find that swimmers that propel either by forward thrust (pullers, e.g., Chlamydomonas) or backward thrust (pushers e.g., Escherichia coli) have the same affinity towards the boundary. However, in the presence of steric interactions, we find that pullers have a greater affinity towards the convex curvature and pushers have a greater affinity towards the concave curvature.