Evaluating the image quality is a very important problem in image and video processing. Numerous methods have been proposed over the past years to automatically evaluate the quality of images in agreement with human quality judgments. The purpose of this work is to present subjective and objective quality assessment methods and their classification. Eleven widely used and recommended by International Telecommunication Union (ITU) subjective methods are compared and described. Thirteen objective method is briefly presented (including MSE, MD, PCC, EPSNR, SSIM, MS-SSIM, FSIM, MAD, VSNR, VQM, NQM, DM, and 3D-GSM). Furthermore the list of widely used subjective quality data set is provided.