Texture is a fundamental characteristic of many types of images, and texture representation is one of the essential and challenging problems in computer vision and pattern recognition which has attracted extensive research attention over several decades. Since 2000, texture representations based on Bag of Words and on Convolutional Neural Networks have been extensively studied with impressive performance. Given this period of remarkable evolution, this paper aims to present a comprehensive survey of advances in texture representation over the last two decades. More than 250 major publications are cited in this survey covering different aspects of the research, including benchmark datasets and state of the art results. In retrospect of what has been achieved so far, the survey discusses open challenges and directions for future research.