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Twisted moiré photonic crystal is an optical analog of twisted graphene or twisted transition metal dichalcogenide bilayers. In this paper, we report the fabrication of twisted moiré photonic crystals and randomized moiré photonic crystals and their use in enhanced extraction of light in light-emitting diodes (LEDs). Fractional diffraction orders from randomized moiré photonic crystals are more uniform than those from moiré photonic crystals. Extraction efficiencies of 76.5%, 77.8% and 79.5% into glass substrate are predicted in simulations of LED patterned with twisted moiré photonic crystals, defect-containing photonic crystals and random moiré photonic crystals, respectively, at 584 nm. Extraction efficiencies of optically pumped LEDs with 2D perovskite (BA)2(MA) n −1PbnI3 n +1 of n = 3 and (5-(2′-pyridyl)-tetrazolato)(3-CF3−5-(2′-pyridyl)pyrazolato) platinum(II) (PtD) have been measured. [ABSTRACT FROM AUTHOR]