Van der Waals heterostructures of twisted or lattice-mismatched two-dimensional transition metal dichalcogenides emerged as rich and versatile platforms for optical studies of many-particle and correlated electron physics. These types of phenomena depend sensitively on the material configurations, including lattice and angular mismatch leading to the formation of moiré-superlattices, or locally and mesoscopically reconstructed domains. While offering a high level of flexibility and tunability for the design of the electronic many-particle states, it also demands accurate descriptions of the underlying fundamental processes. This motivates the main goal of this project, namely to develop comprehensive understanding of the many-body physics in semiconducting van der Waals heterostructures governing their optical response across linear and non-linear regimes. We will address a broad range of density conditions for both bosonic and fermionic types of quasiparticles, such as excitons or electron-hole plasma and their mixtures. Specifically, we aim to understand the impact of dimensionality from effectively two-, one-, and zero-dimensional domains in reconstructed heterostructures on the dynamics and transport of optical excitations. In addition, we will create and control hybrid, interacting moiré exciton states combining strong exciton-exciton and exciton-photon interactions towards tunable dipolar polaritonics. Finally, we will develop experimental and theoretical approaches for the manipulation of electron-exciton and exciton-exciton interactions to realize regimes crossing the border between pure Bose and Fermi gases to trigger formation of distinct many-body phases on demand.