  Many practically relevant materials combine properties of viscous fluids and
elastic solids to viscoelastic behavior. Our focus is on the induced dynamic
behavior of damped finite-sized particulate inclusions in such substances. We
explicitly describe history-dependent interactions that emerge between the
embedded particles. These interactions are mediated by the viscoelastic
surroundings. They result from the flows and distortions of the viscoelastic
medium when induced by the rigid inclusions. Both, viscoelastic environments of
terminal fluid-like flow or of completely reversible damped elastic behavior,
are covered. For illustration and to highlight the role of the formalism in
potential applications, we briefly address the relevant examples of dragging a
rigid sphere through a viscoelastic environment together with subsequent
relaxation dynamics, the switching dynamics of magnetic fillers in elastic gel
matrices, and the swimming behavior of active microswimmers in viscoelastic
solutions. The approach provides a basis for more quantitative and extended
investigations of these and related systems in the future.
