The internet of things (IoT) has been used in a wide range of applications since its emergence, including smart cities, intelligent systems, smart homes, smart agriculture, and healthcare. IoT systems rely on information processing and sharing, where data leakages may jeopardize their security and privacy. On the other hand, quantum computers are poised to solve complex problems that traditional computers cannot. However, due to the fact that the majority of cyber algorithms are based on significant computational complexity, quantum computing poses a substantial threat to the cyber security of global digital infrastructure, including IoT networks, smart cities, banking, and intelligent infrastructure. This chapter discusses potential security and privacy measures for a post-quantum world against threats posed by quantum computing, including post-quantum cryptography, quantum software testing, post-quantum blockchain technology, and architectural considerations for creating post-quantum secure IoT systems.