In medical imaging systems, denoising is one of the important image processing tasks. Automatic noise removal will improve the quality of diagnosis and requires careful treatment of obtained imagery. Computed tomography (CT) and X-Ray imaging systems use the X radiation to capture images and they are usually corrupted by noise following a Poisson distribution. Due to the importance of Poisson noise removal in medical imaging, there are many state-of-the-art methods that have been studied in the image processing literature. These include methods that are based on total variation (TV) regularization, wavelets, principal component analysis, machine learning etc. In this work, we will provide a review of the following important Poisson removal methods: the method based on the modified TV model, the adaptive TV method, the adaptive non-local total variation method, the method based on the higher-order natural image prior model, the Poisson reducing bilateral filter, the PURE-LET method, and the variance stabilizing transform-based methods. Our task focuses on methodology overview, accuracy, execution time and their advantage/disadvantage assessments. The goal of this paper is to provide an apt choice of denoising method that suits to CT and X-ray images. The integration of several high-quality denoising methods in image processing software for medical imaging systems will be always excellent option and help further image analysis for computer-aided diagnosis. Povzetek: Pregledni članek opisuje metode za čiščenje slike, narejene z rentgenom ali CT.