We argue that a key to further advances in the fields of image analysis and compression is a better understanding of texture. We review a number of applications that critically depend on texture analysis, including image and video compression, content-based retrieval, visual to tactile image conversion, and multimodal interfaces. We introduce the idea of "structurally lossless" compression of visual data that allows significant differences between the original and decoded images, which may be perceptible when they are viewed side-by-side, but do not affect the overall quality of the image. We then discuss the development of objective texture similarity metrics, which allow substantial point-by-point deviations between textures that according to human judgment are essentially identical.