Electron fractionalization is a striking quantum phenomenon in which electrons in certain strongly correlated systems appear to break apart into emergent quasiparticles with fractional charge or spin. Fractionalized electrons, known as anyons, are not only of theoretical interest, but can potentially be harnessed for fault-tolerant quantum computing. In this talk, I will describe theoretical ideas and material platforms for finding anyons in two-dimensional materials with flat topological bands. I will then survey recent observations of fractionally quantized anomalous Hall effect in moire materials, which establishes a new states of matter hosting fractionalized electrons. Finally I will discuss the prospect of finding non-Abelian anyons and deep learning fractional electron states with artificial neural network.