By integrating mesoscale models for hydrodynamics and micromechanics, we examine the fluid-driven motion of microcapsules on compliant surfaces. The capsules, modeled as fluid-filled elastic shells, represent polymeric microcapsules or biological cells. We examine the motion of these capsules on flat, mechanically uniform surfaces, mechanically patterned surfaces that contain alternating regions of hard and soft domains, and topologically patterned surfaces, i.e., a corrugated substrate and a substrate that encompasses a regular array of compliant posts. We isolate conditions where the mechanically and topographically patterned surfaces can transmit "stop" and "go" instructions, causing the capsules to halt at specific locations on the substrate, and with an increase in the imposed flow velocity, to resume moving. In the case of the corrugated surfaces, varying the size of the asperities permits significant control over the translational velocity of a capsule for a given shear rate. For surfaces containing regular arrays of compliant posts, the substrates also affect the capsules' gait, causing them to "crawl", "walk", or "jump". The latter behavior could promote the intermixing of reactants that are encapsulated within the microcapsules. These topographically patterned surfaces can also be utilized to sort capsules accordingly their size. Such control over capsule dynamics can enable the fabrication of arrays of mobile microreactors and facilitate various biological assays.