Optimal transport is a long-standing theory that has been studied in depth from both theoretical and numerical point of views. Starting from the 50s this theory has also found a lot of applications in operational research. Over the last 30 years it has spread to computer vision and computer graphics and is now becoming hard to ignore. Still, its mathematical complexity can make it difficult to comprehend, and as such, computer vision and computer graphics researchers may find it hard to follow recent developments in their field related to optimal transport. This survey first briefly introduces the theory of optimal transport in layman's terms as well as most common numerical techniques to solve it. More importantly, it presents applications of these numerical techniques to solve various computer graphics and vision related problems. This involves applications ranging from image processing, geometry processing, rendering, fluid simulation, to computational optics, and many more. It is aimed at computer graphics researchers desiring to follow optimal transport research in their field as well as optimal transport researchers willing to find applications for their numerical algorithms.