Moiré superlattices of two-dimensional (2D) materials are an emerging platform for studying new physical phenomena with high tunability. Strong excitonic responses in transition metal dichalcogenides (TMDs) allow optical access to the wealth of physics. In this talk, I will present our recent results about interactions between excitons and charge carriers trapped in moiré potentials. We have discovered novel exciton many-body ground states composed of moiré excitons and correlated electron lattices, resulting from new interaction between exciton and charges enabled by unusual quantum confinement in 2D moiré superlattices. The interaction further enriches the magnetic phases in such moiré superlattices. We have observed that the spin-spin interactions between moiré trapped holes can be drastically tuned by optical excitation power. The mechanism points to the unique excitons-mediated long-range exchange interaction between moiré trapped carriers. This discovery adds a new and dynamic tuning knob to the rich many-body Hamiltonian of moiré quantum matter. Our work provides the framework for understanding and engineering electronic and excitonic states in moiré quantum matters.