The emerging Self-Sovereign Identity (SSI) techniques, such as Decentralized Identifiers (DIDs) and Verifiable Credentials (VCs), move control of digital identity from conventional identity providers to individuals and lay down the foundation for people, organizations, and things establishing rich digital relationship. The existing applications of SSI mainly focus on creating person-to-person and person-to-service relationships, whereas person-to-device and device-to-device interactions have been largely overlooked. In this paper, we close this gap by identifying a number of key challenges of applying SSI to the Internet of Things (IoT) and providing a comprehensive taxonomy and usage of VCs in the IoT context with respect to their validity period, trust and interoperability level, and scope of usage. The life-cycle management of VCs as well as various optimization techniques for realizing SSI in IoT environments are also addressed in great detail. This work is a noteworthy step towards massive adoption of SSI for securing existing and future IoT applications in practice.