Abstract. In modern steganography, designing a distortion function to get the cost for every cover elements is an open problem. Many researchers have proposed a lot of different valuable distortion functions from different point of view. In this paper, the distortion function are classified to three categories, the first is from the view of steganalysis to design distortion function, the second is the distortion function are designed by filters bank, the third is the distortion function is designed begin with a well model of images. It is hoped that the summarized result in this paper is valuable for designing other better distortion function.