Abstract—Transform-based image coding has been the mainstream for many years, as witnessed in from the early effort in JPEG to the recent advances in HD Photo. Traditionally, a 2-D transform used in image coding is always implemented separately along the vertical and horizontal directions, respectively. However, it is usually true that many image blocks contain oriented structures (e.g., edges) and/or textures that do not follow either the vertical or horizontal direction. The traditional 2-D transform thus may not be the most appropriate one to these image blocks. This well-known fact has recently triggered several attempts towards the development of directional transforms so as to better preserve the directional information in an image block. Some of these directional transforms have been applied in image coding, demonstrating a significant coding gain. This paper presents an overview of these directional transforms as well as a discussion of some existing problems and their potential solutions. I.