Real-valued separable wavelets and framelets are known to have some shortcomings; in particular,they lack directionality for high dimensional problems such as image and video processing.In this talk,we show that directionality can be greatly improved by using complex tight framelets.We first introduce directional complex tight framelets and then we explore several exciting applications of directional complex tight framelets to image denoising and image inpainting.Numerical algorithms will be developed and we shall show that directional complex tight framelets have superior performance compared with many other transform-based methods.