Electronic commerce, or e-commerce, is the buying and selling of goods and services, or the transmitting of funds or data online. E-commerce platforms come in many kinds, with global players such as Amazon, Airbnb, Alibaba, eBay and platforms targeting specific geographic regions. Information retrieval has a natural role to play in e-commerce, especially in connecting people to goods and services. Information discovery in e-commerce concerns different types of search (e.g., exploratory search vs. lookup tasks), recommender systems, and natural language processing in e-commerce portals. The rise in popularity of e-commerce sites has made research on information discovery in e-commerce an increasingly active research area. This is witnessed by an increase in publications and dedicated workshops in this space. Methods for information discovery in e-commerce largely focus on improving the effectiveness of e-commerce search and recommender systems, on enriching and using knowledge graphs to support e-commerce, and on developing innovative question answering and bot-based solutions that help to connect people to goods and services. In this survey, an overview is given of the fundamental infrastructure, algorithms, and technical solutions for information discovery in e-commerce. The topics covered include user behavior and profiling, search, recommendation, and language technology in e-commerce.