Metasurfaces composed of dielectric nanoresonators with subwavelength thickness allow for strong control over the properties of light in transmission and reflection. In the last years, this control has been extended to classical parametric processes like sum-frequency generation, with the engineering of polarization and directionality of the generated light and the enhancement of the nonlinear conversion efficiency. These properties make nonlinear metasurfaces promising also for quantum technologies, especially for creating very thin, yet efficient and highly tailorable sources of photon pairs. This perspective is encouraged by recent observations of photon-pair spontaneous parametric generation in nonlinear metasurfaces. However, the true strength of metasurfaces, which stems from their open-system nature with access to numerous photonic degrees of freedom, makes the related modeling of a nonlinear quantum process very challenging. Yet, such a description is needed to control this broadband generation and therefore engineer the properties of the down-converted pairs towards specific quantum states. To date, this lack of a model has hindered both a fundamental insight in the operation of metasurface photon-pair sources and their development for quantum optical technologies. The goal of MEGAPHONE is therefore to establish a methodology for an accurate, but also computationally efficient and physically insightful description of photon-pair generation in dielectric metasurfaces, and use this methodology to create metasurfaces with tailored biphoton quantum states, and drastically improved generation efficiencies with respect to the state of the art. To this end, we will resort to quasinormal modes, which are a class of modal expansion suited for describing electromagnetic systems with a large amount of outward radiation or internal losses. MEGAPHONE will investigate pair generation from nonlinear metasurfaces in different operating regimes, with periodic and non-periodic arrangements of both non-interacting and interacting dielectric nanoresonators. Through a combination of analytical and numerical approaches, MEGAPHONE will both investigate the open-system effects that can potentially decrease the fidelity of the generated state with respect to the ideal targeted quantum state, and single out possible approaches for increasing it. Based on these theoretical grounds, the MEGAPHONE partners will fabricate and experimentally demonstrate concrete examples of metasurface photon-pair sources designed for generating polarization entangled states in the well-established AlGaAs technological platform of the French partner, and spatially correlated states in the well-established LN technological platform of the German partner. The results of this project will open the way for the broad development of metasurface photon-pair sources in different areas of photonic quantum technologies, from free-space quantum communication to quantum imaging and sensing.