Flat and nearly flat bands suppress single-particle kinetic energy, bringing electron correlations, exchange interactions, and wave-function geometry to the forefront of low-energy physics. This review argues that bandwidth alone is insufficient for identifying genuine flat-band platforms; band isolation, wave-function structure, and experimentally observable interaction-driven signatures must be assessed together. We summarize the main routes to flat-band formation, including geometric frustration, destructive interference, multi-orbital hybridization, structural distortion, and moire superlattices. On this basis, we show that flat bands cannot be reduced to ordinary narrow bands with a high density of states. Instead, their distinctive physics is shaped by compact localized states, singularity structures, and quantum geometry, which together govern the emergence of diverse many-body responses, including ferromagnetism, correlated insulators, superconductivity, and topological fractional states across kagome materials, moire systems, and artificial lattices. Finally, we translate these physical principles into a practical four-layer framework for identifying genuine flat-band systems.
Liu et al. (Tue,) studied this question.