We discuss a new class of high-Q nonlocal metasurfaces composed of weakly coupled optical waveguides with a periodically broken translational symmetry. The physics of such metasurfaces can be understood with the concept of coupled-resonator optical waveguides (CROWs) developed earlier for in-plane propagation in arrays of optical microresonators and photonic crystal cavities, allowing to realize photonic flatbands that exhibit uniform response to the resonant light across a wide range of incident angles. We suggest several realizations of this concept for anisotropic metasurfaces and demonstrate experimentally how such CROW-inspired metasurfaces can be employed to achieve unidirectional and bidirectional linear polarization flatbands, as well as chiral flatbands that are highly selective to the circular polarization of the incoming light.