In digital coherent imaging and measurement systems, the image/fringe pattern quality is severely degraded by multiplicative uncorrelated noise, called speckle, resulting due to the coherent nature of the light source, which restricts the development of several applications of these systems in various fields. Digital holography, holographic interferometry, speckle metrology, and shearography are the most revealing non-invasive imaging and measurement tools in many areas including scientific, engineering, biomedical, and industrial applications. However, the presence of undesired speckle noise in the processed image/phase distribution may lead to ambiguity in the observation or analysis of the associated physical parameters, and thus, limit their applications in many fields. To overcome this problem, a variety of algorithms/methods/techniques have been developed to eliminate the inherent speckle-noise introduced in the images/phase distribution obtained from these systems, depending on the requirement and the understanding of the noise characteristics. The speckle denoising is the pre-processing step in these systems and their performance determines the accuracy of the measurand physical parameter. This review article aims to cover some important state-of-art speckle denoising algorithms. For the purpose of demonstration, the performance and comprehensive study of these algorithms are evaluated on simulation and experimental data.