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In flat bands of two-dimensional materials, the mass of charge carriers increases dramatically and the Coulomb energy of the charge carriers can be much larger than the quenched kinetic energy. When the flat band is partially filled, electron-electron interactions can drive electrons to form exotic correlated phases, such as quantum Hall ferromagnetism, fractional quantum Hall effect, superconductivity, and quantum anomalous Hall effect. Therefore, flat bands in two-dimensional materials have attracted much attention very recently. In the past few years, the strongly correlated phenomena in flat bands have become a hot topic in community of condensed matter physics. There are several different methods, such as using a perpendicular magnetic field, introducing strained structures, and introducing a twist angle, to realize the flat bands in two-dimensional materials. In this review article, we summarize the methods to realize flat bands in two-dimensional systems and introduce the related novel electronic states when the flat band is partially filled.
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