In the Internet of things (IoT) era, user authentication is an essential to ensure the security of connected devices and the customization of passive services. However, conventional knowledge-based and physiological biometric-based authentication systems (e.g., password, face recognition, and fingerprints) are susceptible to shoulder surfing attacks, smudge attacks and heat attacks. The powerful sensing capabilities of IoT devices including smartphones, wearables, robots and autonomous vehicles enable the continuous authentication (CA) based on behavioral biometrics. Artificial Intelligence (AI) approaches hold significant promise in sifting through large volumes of heterogeneous biometrics data to offer unprecedented user authentication and user identification capabilities. In this survey paper, we outline the nature of continuous authentication in IoT applications, highlight the key behavioral signals, and summarize the extant solutions from an AI perspective. Based on our systematic and comprehensive analysis, we discuss the challenges and promising future directions to guide the next generation of AI-based continuous authentication research.