  Flat bands - single-particle energy bands - in tight-binding networks have
attracted attention due to the presence of macroscopic degeneracies and their
extreme sensitivity to perturbations. This makes them natural candidates for
emerging exotic phases and unconventional orders. The challenging part however
is to construct flat band networks, whose existence relies on symmetries and
fine-tuning. In this review we consider the recently proposed systematic ways
to construct flat band networks based on symmetries or fine-tuning. We then
discuss how the fine-tuning constructions can be further extended, adapted or
exploited in presence of perturbations, both single-particle and many-body.
This strategy has lead to the discovery of non-perturbative metal-insulator
transitions, fractal phases, nonlinear and quantum caging and many-body
nonergodic quantum models. We discuss what implications these results may have
for the design of fine-tuned nanophotonic systems including photonic crystals,
nanocavities, and metasurfaces.
