  We reveal that metasurfaces created by seemingly different lattices of
(dielectric or metallic) meta-atoms with broken in-plane symmetry can support
sharp high-$Q$ resonances that originate from the physics of bound states in
the continuum. We prove rigorously a direct link between the bound states in
the continuum and the Fano resonances, and develop a general theory of such
metasurfaces, suggesting the way for smart engineering of resonances for many
applications in nanophotonics and meta-optics.
