  Bound states of two interacting particles moving on a lattice can exhibit
remarkable features that are not captured by the underlying single-particle
picture. Inspired by this phenomenon, we introduce a novel framework by which
genuine interaction-induced geometric and topological effects can be realized
in quantum-engineered systems. Our approach builds on the design of effective
lattices for the center-of-mass motion of two-body bound states
(\emph{doublons}), which can be created through long-range interactions. This
general scenario is illustrated on several examples, where flat-band
localization, topological pumps and higher-order topological corner modes
emerge from genuine interaction effects. Our results pave the way for the
exploration of interaction-induced topological effects in a variety of
platforms, ranging from ultracold gases to interacting photonic devices.
