Metasurfaces, benefiting from the flexibility in engineering the resonance, near-field, symmetry, and scattering properties of individual building blocks, are promising not only for a wide range of practical applications in the classical linear optical regime, but also facilitate research into new unconventional areas. Very recently, we have been witnessing the second quantum revolution in which quantum information processing and computation are becoming a reality. In this review, we will focus on some of the emerging developments of metasurfaces that work in the nonlinear, non-Hermitian, nonclassical, or quantum regime. We review some of the common principles shared by the development of these metasurfaces, including local field enhancement and the consideration of structure, lattice, and time-reversal symmetries.