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Computer-generated holography (CGH) has demonstrated significant promise as a display technique, with benefits including the ability to display images supporting true refocus at diffraction-limited resolution at the eye, and brightness levels meeting the most demanding requirements for outdoor augmented-reality applications. Whereas historically the computational load required for CGH has been a barrier to wider adoption, this has been demonstrated to be within reach of modern mobile devices for many real-world use cases. However, one area which remains a concern for CGH, as with other laser-based display technologies, is the reduction of noise arising from coherent illumination, loosely known as laser speckle. In this work we identify and model the modes in which Speckle affects the apparent visual quality of images generated using 2D and 3D holography and compare the effectiveness of known and theoretical optical and algorithmic techniques for speckle reduction. Reduction of speckle noise is of particular interest to CGH, but there is significant extant literature on speckle-reduction techniques from other disciplines, such as microscopy using coherent illumination, and laser metrology. These techniques are examined and their applicability to CGH considered. Approaches including a diffusing element are typically limited to 2D CGH, as they destroy the coherence required to support multiple depth planes. For techniques that in a broad sense act on the spatial/temporal coherence of the system to reduce speckle, such as use of a superluminescent light emitting diode (SLED), or a moving optical element, a trade-off between speckle reduction and reduced resolution must be found. In addition, we review the impact of algorithmic techniques used in CGH to reduce speckle-like noise during the generation of holograms, and compare the effectiveness of these techniques to hardware-based solutions.