The fashion industry is one of the most active and competitive markets in the world, manufacturing millions of products and reaching large audiences every year. A plethora of business processes are involved in this large-scale industry, but due to the generally short life-cycle of clothing items, supply-chain management and retailing strategies are crucial for good market performance. Correctly understanding the wants and needs of clients, managing logistic issues and marketing the correct products are high-level problems with a lot of uncertainty associated to them given the number of influencing factors, but most importantly due to the unpredictability often associated with the future. It is therefore straightforward that forecasting methods, which generate predictions of the future, are indispensable in order to ameliorate all the various business processes that deal with the true purpose and meaning of fashion: having a lot of people wear a particular product or style, rendering these items, people and consequently brands fashionable. In this paper, we provide an overview of three concrete forecasting tasks that any fashion company can apply in order to improve their industrial and market impact. We underline advances and issues in all three tasks and argue about their importance and the impact they can have at an industrial level. Finally, we highlight issues and directions of future work, reflecting on how learning-based forecasting methods can further aid the fashion industry.