Curvelet transformation, an extension and latest development of Wavelet and Ridgelet transformation, is a kind of multiscale, multidirectional and anisotropic transformation, and is very suitable for representing the image edge. Both the fundamental research and practical application of curvelet transformation have progressed greatly, since it was introduced. This paper presents the applications of curvelet transformation on image fusion, denoising, compression sensing and texture feature extraction in medical image processing. This review is purposed useful for developing the curvelet transformation theory and exploring more efficient medical image processing methods.