One of the most exotic phenomena in condensed matter systems is the emergence of fractionalized particles. However, until now, only a few experimental systems are known to realize fractionalized excitations. This calls for more systematic ways to find and understand systems with fractionalization. One natural starting point is to look for an exotic quantum criticality, where the fundamental degrees of freedom become insufficient to describe the system accurately. Furthermore, understandings in exotic quantum critical phenomena would provide a unified perspective on nearby gapped phases, i.e. a guiding principle to engineer the system in a desirable direction that may host anyons. In this talk, I would present my works on quantum phase transitions between fractional Chern/Quantum Hall insulators tuned by the strength of lattice potential [PRX 8, 031015 (2018)]. Here, the low-lying excitations are already fractionalized; therefore, the deconfined fractional excitations follows more naturally, which is described by Chern-Simons quantum electrodynamics. The numerical results using iDMRG as well as theoretical analysis of their emergent critical properties would be presented. In the end, I would discuss their spectroscopic signatures, providing a full analysis of experimental verification. If time allows, I would talk about my other recent works on quantum magnets in 1+1 dimension.