Metasurfaces are ushering in an era of multifunctional control over optical wavefronts realized with ultrathin planarized devices. Recent advances have been enabling unprecedented control over the frequency response of these surfaces, suggesting that the future of flat optics may tailor both spectral and spatial degrees of freedom in highly multispectral and multifunctional devices. Diffractive nonlocal metasurfaces are opening new opportunities in this direction: they leverage symmetry-protected scattering from quasi-bound states in the continuum and, by spatially manipulating controlled geometric perturbations, they support ultrasharp optical responses with wavefront-manipulating features. Encoded in nonlocal (i.e., spatially extended) resonant modes, the resulting response is observed exclusively within the bandwidth of the resulting Fano resonance, affording ideal features for a wide range of applications. In this perspective, this novel class of metasurfaces are discussed in the broader context of flat optics, highlighting their peculiar operation in contrast to relevant predecessors, and highlighting the opportunities for future advancement and applications. In particular, it is emphasized that nonlocality and selectivity are inherently related, but that spectral and spatial selectivity can be independently tuned in suitably tailored metasurfaces. In turn, this freedom allows the design and implementation of both wavefront-shaping and wavefront-selective devices. The novel optical responses, combined with the compatibility with rational design, herald new prospects for active, nonlinear and quantum metasurfaces, ultrathin devices for augmented reality, and compact tailored optical sources.