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Computer-generated holography, a technique for synthesizing holographic images using computer algorithms, has advanced with developments in computational methods and digital technologies. However, the traditional methods struggle to achieve computational speed and accuracy, simultaneously. To address this, this dissertation explores the integration of deep neural networks with semi-analytical methods to enhance the hologram design and its performance across various applications. We develop solvers based on physics-informed neural networks to enable phase optimization and mitigate errors due to due to system noise and imperfections. In the first project, a novel layer-based holography approach combines deep Convolutional Neural Networks (CNNs) with a Bessel beam expansion known as Frozen Waves (FWs) to generate images on longitudinal planes, perpendicular to holographic displays. Two distinct solvers are developed: one based on analytical simulations for scalability, and another using numerical Angular Spectrum Method (ASM) for enhanced flexibility and accuracy. Additionally, a Look up Table (LuT) method was developed to accelerate the numerical simulations. The second project provides an alternative method by combining neural networks with a Plane Wave (PW) expansion. This hybrid system exhibits improved accuracy and computational efficiency compared to the previous method utilizing FWs. Experimental data demonstrates the effectiveness of this method in practical holographic setups. In the third project, our framework was applied to Orbital Angular Momentum (OAM)-multiplexed holography in the spatial frequency domain. This system achieves higher multiplexing capacity and lower error levels as compared to previously proposed methods, notable using phase-only holograms. Furthermore, a realistic, parameterized propagation model of a Fourier domain holography system was developed using a Camera-In-The-Loop (CITL) approach. This model, which captures non-idealities and noise models, was incorporated in the hologram design pipelines to improve image quality in real-world settings. Ultimately, this research contributes to computer-generated holography by showcasing new applications of machine learning to enhance traditional methods. The proposed techniques offer improvements in image quality and computational speed, suitable for real-time applications in areas such as augmented reality, imaging and optical communication systems.