Quantum simulators may provide unprecedented insights into physical phenomena and have the potential to enable radically new technologies. Analog dynamical quantum simulators constitute a class of quantum machines outperforming classical computers. In this project POLISIMULATOR, we undertake a two-fold approach: We devise versatile and practical platforms for dynamical quantum simulators with lattices of semiconductor exciton polaritons; and we conduct an interdisciplinary research programme to build quantum devices and assess their computational capabilities. We then use those devices to probe important questions in fundamental and applied physics, ranging from technology-relevant problems concerning dynamics of coherent and dissipative transport processes, to long-standing challenges in physics of non-equilibrium many-body phenomena.