History shows that the research for novel structures is one of the most important goals for materials science and engineering. In the past few years, moiré van der Waals systems have attracted considerable attention from the materials research community due to the novel emerging physics enabled by such structures. Periodic moiré patterns lead to superlattices that can induce structural altering and band transformations, resulting in new phenomena including moiré excitons, unconventional superconductivity, and Mott-like insulation. Due to the intrinsic similarities between photonic systems and condensed matter systems, moiré photonic systems also introduce an additional degree of freedom to the tuning of the system and have promised exotic behaviors with potential breakthroughs for photonic studies. Moreover, the research for moiré photonic systems may also guide the exploration of moiré van der Waals structures and broaden the field of moiré physics. However, a comprehensive model to characterize moiré photonic systems is still lacking, impeding further research in this direction.To overcome this problem, I developed a theoretical model based on twisted bilayer photonic crystals (TBPC) to describe the coupling mechanism and calculate the photonic band structure in moiré photonic systems. A modified coupled mode theory is developed to take into account high coupling orders in the reciprocal space and optical losses, followed by the formulation of a continuum description for optical modes. Using this model, the photonic band structure is achieved, and photonic magic angles are discovered with signatures of photonic flat bands, zero light group velocities, and spiky photonic density of states. Moreover, a phase diagram of photonic magic-angle effects as a function of the twist angle and the interlayer separation is established and found to be consistent with full-wave simulations. The evolution of the photonic magic angle with the interlayer separation reveals a striking similarity between the TBPC and the electronic twisted bilayer graphene, presenting the similarities between photonic systems and condensed matter systems. The remarkable design flexibility of electromagnetic response from the photonic systems makes TBPC an exceptional platform for a better understanding of moiré physics in general, including new configurations that are not easily achievable in electronic systems. Next, based on the theoretical model in the previous work, I analyzed the chirality of TBPC, and theoretically showed the existence of optical vortex emission from TBPC. An interlayer channeling model is formulated based on coupled mode theory to demonstrate that the optical vortex emission originates from the twist-enabled coupling between the bound state in the continuum (BIC) mode and the guided resonances. Moreover, the optical vortex generation in TBPC is robust against disturbance in geometric parameters, making TBPC a promising platform for controllable vortex generation, and providing new routes to design stable vortex lasers. Furthermore, the incorporation of TBPC and micro/nanoelectromechanical systems (MEMS/NEMS) could lead to the creation of tunable vortex beams with adjustable topological orders, beam center positions, divergence angles, etc. This could lead to breakthroughs in many applications, such as super-resolution imaging, optical communication, micromanipulation, and quantum information processing. Besides the application in vortex generation, the twist-enabled coupling mechanism in TBPC provides a tunable interlayer channel to connect BIC modes to the free space. This will not only benefit the development of BIC study, but also broaden the field of moiré photonics. The optical vortex generation in the moiré photonic system has no analog in the moiré van der Waals system yet. Due to the intrinsic similarities between photonic systems and condensed matter systems, this work may also guide the exploration of orbital angular momentum in moiré van der Waals structures. In summary, I have formulated a theoretical model to describe the coupling mechanism and calculate the photonic band structure in moiré photonic systems. Using this model, I first discovered the existence of photonic flat bands in twisted bilayer photonic crystals (TBPCs). Then, I theoretically show the generation of robust optical vortex radiation in TBPCs. My work builds the basis of the moiré photonic studies and guides the exploration of moiré van der Waals structures. They have the potential to not only improve the understanding of fundamental physics but also lead to substantial breakthroughs in many applications, such as super-resolution imaging, optical communication, micromanipulation, and quantum information processing.