Controlling quantum correlations in many-body systems in is one of the major challenges in solid-state physics, and of critical importance for enabling applications in integrated quantum technologies. A material class that is particularly suitable to study and control the physics of correlated Bosons and Fermions are van der Waals heterostructures. These structures can be realized bottom up, layer by layer, with precision on the atomic level. Uniquely, their most fundamental electronic and quantum-optical properties can controlled via the rotation angle (‘the twist’) between the layers. This twistronic material engineering is especially suited to tailor emergent quantum correlations in van der Waals heterostructures and to control the collective quantum behavior in this novel material class. It is the ambition of the “Dual-Twist” project to explore emergent quantum phases of Coulomb- correlated carriers and to control their interaction with precisely tailored light-fields in twistronically engineered quantum materials. The project synergizes the emergent technique of “twistronics” to functionalize van-der-Waals heterostructures on the quantum level with the approach to utilize optical cavities to engineer quantum materials via dressing them with electromagnetic fields. Our quantum-optical investigations will provide pathways to control collective phenomena of Bose-Fermi mixtures in microcavities, correlated magnetism, collective quantum phases and strongly interacting ‘liquid light’. Dual Twist utilizes a cavity-based quantum simulation approach to reach a deeper level of understanding in our material-based experiments. The project will develop a versatile technology to simulate the quantum behavior of interacting bosons in twist-tunable lattices of non-linear photons. Thus, it will expand our insight into the Moiré physics of correlated Bosons and will provide fundamental answers regarding their applicability in quantum information.