Computer-generated holography (CGH) is a technique of digitally generating holograms from real-world or synthetic three-dimensional (3D) objects with numerical computation. However, direct calculation, generally referred to as ray tracing, of a computer-generated Fresnel hologram (CGFH) is computationally intensive. Moreover, real-time hologram generation can hardly be realized in practice. In recent decades, the rapid development and commercial availability of specialized high-speed digital processing hardware, such as Central Processing Unit (CPU), Graphic Processing Unit (GPU), and Field Programmable Gate Array (FPGA), have brought real-time hologram generation closer to reality. Despite the aid of hardware technology, providing real-time generation for 3D holographic video, especially high-resolution video, remains difficult. Therefore, apart from the use of hardware for acceleration, we explored superior algorithms to approximate the object beam at the hologram plane, so calculations can be significantly simplified and generation time can be greatly reduced. Hence, real-time holographic video can be achieved. This thesis reports two fast generation approaches of CGFH, namely, "Sub-Line-Based approach" and "Interpolated Wavefront Recording Plane (IWRP) approach" to alleviate and overcome the problems stated above. For the Sub-Line-Based approach, the generation process is divided into two stages. In the first stage, a multi-bank FIR filter architecture is proposed to generate the sub-lines. In the second stage, the sub-lines are expanded vertically to form a full Fresnel hologram. Generation of the sub-lines is realized with a FPGA device, while the expansion process is encapsulated as a pair of 1D Fast Fourier Transform (FFT) operations that is conducted in the GPU. For the holograms generated based on the sub-line approach, the resolution of the reconstructed images are higher, but limited to horizontal-parallax-only information. For the IWRP approach, the generation process is divided into two stages. In the first stage, down-sampling and interpolation are applied to the object scene. Subsequently, the latter is employed to generate an IWRP based on a computation-free table lookup method. In the second stage, a full Fresnel hologram is obtained by expanding, through computation of the wave propagation, the IWRP to a hologram. This process is implemented with a pair of 2D FFT operations which is realized with the GPU. For the holograms generated based on the IWRP approach, the resolution of the reconstructed images are relatively lower due to the down-sampling of the object scene, but capable of maintaining full parallax information. Experimental results reveal that both approaches enable the Fresnel holograms to be generated at a video frame rate of 33 and 40 frames per second, respectively.