Holographic displays have often been touted as the ultimate 3-D display, not the least because they are the only known method so far that can recreate the exact light wave from 3-D objects having been recorded in a hologram. Computer-generated holograms (CGH) can be computed for any imaginary object based on a mathematical description. It is an extremely demanding and complex task to generate CGHs that produce realistic reconstructions with full-parallax, occlusion and shadowing etcetera. Despite decades of advancements in computer technology since the inception of the CGH, the complexity of computing light transportation and interaction is such that generating holograms of photorealistic 3-D scenes in real-time still remains unattainable. This thesis describes the simulation of light-object interaction, occlusion, and light wave propagation for the purpose of creating CGHs. Two algorithms that harness the parallel-computing capability of a graphics processing unit for fast CGH generation are presented. The key insight is to divide the CGH computation process into small, independent computation tasks that can be executed concurrently. Different paths for parallelisation are considered, as well as methods of approximation to seek a balance between computational complexity and visual quality. The optical reconstruction of CGHs is analysed to identify the source of reconstruction errors and their impact on the visual quality of the reconstructed images. The study proves that Fourier CGHs can be used to display rich 3-D content with considerable depth and full parallax just like any other types of hologram.