In this dissertation, I report the results of my research on twisted moiré photonic crystals which can be formed through multi-beam holographic interference without a physical rotation and later fabricated by electron-beam lithography. Their optical properties, such as photonic bandgaps, multiple resonance modes, and quality factor are presented. Randomized moire photonic crystals in lattice are also studied. The applications of moire photonic crystals in improving light extraction efficiency are simulated and verified in light emitting devices. Furthermore, I simulated the light extraction efficiency in OLED when the Al layer is patterned with a triangular GPSC, square moiré PhC with defects in the uniform area, and random locations of the photonic lattice, and obtain light extraction efficiency of 78.9%, 79.9%, 81.7%, respectively. Also, the ratios of photoluminescence intensity of LED integrated with twisted moiré PhCs and random moiré PhCs over that without moiré PhCs are measured to be (1.3-1.9) and 1.74, respectively, in a good agreement with simulated ratios of 1.69 and 1.8.