This review article provides a comprehensive survey on state-of-the-art impulse and Gaussian denoising filters applied to images and summarizes the progress that has been made over the years in all applications involving image processing. The random noise model in this survey is assumed to be comprised of impulse (salt and pepper) and Gaussian noise. Different noise models are addressed, and different types of denoising filters are studied in terms of their performance on digital images and in their various practical implications and domains of application. A comprehensive comparison is performed to cover all the denoising methods in details and the results they yield. With this extensive review, researchers in image processing will be able to ascertain which of these denoising methods will be best applicable to their research needs and the application domain where such methods are contemplated for implementation.