A hologram can produce all the 3D depth cues that the human visual system uses to interpret and perceive real 3D objects. As such it is arguably the ultimate display technology. Computer generated holography, in which a computer calculates a hologram that is then displayed using a highly complex modulator, combines the ultimate qualities of a traditional hologram with the dynamic capabilities of a computer display producing a true 3D real image floating in space. This technology is set to emerge over the next decade, potentially revolutionizing application areas such as virtual prototyping (CAD-CAM, CAID etc.), tactical information displays, data visualization and simulation. In this paper we focus on the computational challenges of this technology. We consider different classes of computational algorithms from true computer-generated holograms (CGH) to holographic stereograms. Each has different characteristics in terms of image qualities, computational resources required, total CGH information content, and system performance. Possible trade- offs will be discussed including reducing the parallax. The software and hardware architectures used to implement the CGH algorithms have many possible forms. Different schemes, from high performance computing architectures to graphics based cluster architectures will be discussed and compared. Assessment will be made of current and future trends looking forward to a practical dynamic CGH based 3D display.