Atomically thin transition metal dichalcogenides (TMDs) are 2D semiconductors with tightly bound excitons and correspondingly strong light–matter interactions. Owing to the weak van der Waals bonding between layers, TMDs can be isolated and stacked together to form synthetic heterostructures with emergent electronic and excitonic properties. In this Review, we focus on the emergent exciton physics in moiré superlattices and in TMD heterobilayers coupled to optical cavities, where exciton behaviour can be dramatically modified by the environment. In moiré superlattices, a small twist angle or lattice mismatch between the layers introduces a periodic variation in the interlayer alignment that leads to exciton localization, modified optical selection rules and strong correlations. In cavity–heterostructure systems, light–matter interaction is enhanced and exciton states can couple to the cavity to form exciton-polaritons, whose properties depend on the specific TMD layers involved and their alignment. Here, we discuss recent theoretical and experimental progress towards realizing exotic exciton states in TMD heterobilayers and comment on future scientific and technological directions.