This paper reviews studies of wavelet transform used in image denoising. Image denoising is an indispensable part in image processing, and plays an important role in the field of computer vision. As there is only a single scale in the frequency domain, only a general information can be extracted from the image. The multi-scale and multi-resolution features of wavelet domain make it possible for image denoising to be conducted at different scales. For a better understanding of image denoising, this paper first discusses briefly the mathematical model of image noise, the basic principles and the traditional methods used for image denoising and then, the image denoising theory based on wavelet transform. Three kinds of image denoising methods commonly used in wavelet demain are highlighted, as well as, the advantages and disadvantages of these methods. Finally, the recent development of the wavelet de-noising is reviewed.