The fashion industry is on the verge of an unprecedented change. Fashion applications are benefiting greatly from the development of machine learning, computer vision, and artificial intelligence. In this article, we present an overview of three major topics of fashion and associated state-of-the-art techniques: 1) fashion analysis, including popularity prediction and fashion trend analysis; 2) fashion recommendation, including fashion compatibility and outfit matching; and 3) fashion synthesis, including makeup transfer and virtual try-on. Problem formulations, method comparisons, and evaluation metrics are illustrated for each topic of fashion research. Additionally, promising directions for development in each area are outlined to inspire future research.