Current sound-based practices and systems developed in both academia and industry point to convergent research trends that bring together the field of Sound and Music Computing with that of the Internet of Things. This paper proposes a vision for the emerging field of the Internet of Sounds (IoS), which stems from such disciplines. The IoS relates to the network of Sound Things, i.e., devices capable of sensing, acquiring, processing, actuating, and exchanging data serving the purpose of communicating sound-related information. In the IoS paradigm, which merges under a unique umbrella the emerging fields of the Internet of Musical Things and the Internet of Audio Things, heterogeneous devices dedicated to musical and nonmusical tasks can interact and cooperate with one another and with other things connected to the Internet to facilitate soundbased services and applications that are globally available to the users. We survey the state of the art in this space, discuss the technological and non-technological challenges ahead of us and propose a comprehensive research agenda for the field.