In the Internet of Things (IoT), various devices operate collaboratively in collecting data, relaying information to one another, and processing information intelligently. Due to interactions and dependencies between the IoT devices, the malfunction of one device may trigger a cascade of unexpected and often undesired state changes of other devices, introducing or accelerating catastrophic cascading failures. Understanding the causes of cascading failures and modeling their behavior and effects is crucial for guaranteeing the reliability of IoT systems and delivering the desired quality of service. This article systematically reviews cascading failures modeling and reliability analysis methodologies, as well as mitigation strategies for building the resilience of IoT systems against cascading failures. The review covers diverse IoT applications, from smart grids to smart homes, from sensor networks to IoT cloud computing, and from transportation networks to interdependent infrastructure networks. Opportunities and open research issues are also discussed in relation to restrictions of the current cascading failure models and methods, and potential new technologies and complexity of the constantly evolving IoT systems.