Fashion is a field at the border of art and industry, combining elements of creative spontaneity in a unexpected ways, based on various sources of inspiration. It takes a human to create a clothing and a celebrity to make it fashionable. Real fashion world, designers and creative consumers (street fashion) provide an eclectic ever-changing content that science and technology are trying to optimize in order to increase sales and decrease the waste of over-production. In this talk we provide an overview of fashion big data problems: forecasting fashion trends, influencer analytics, visual search, natural language processing, style recommendation algorithms and the need to understand the natural life-cycle of a fashion garment before applying science in order to accelerate or alter it. Also, we will share some examples of collaboration projects between giants of technology and academics exploring the potential of quantifying fashion data.