The Web of Things extends the Internet of Things by leveraging Web-based languages and protocols to access and control each physical object. In this article, the authors summarize ongoing work promoting the concept of an avatar as a new virtual abstraction to extend physical objects on the Web. An avatar is an extensible and distributed runtime environment endowed with an autonomous behavior. Avatars rely on Web languages, protocols, and reason about semantic annotations to dynamically drive connected objects, exploit their capabilities, and expose user-understandable functionalities as Web services. Avatars are also able to collaborate together to achieve complex tasks.