As cryptographically relevant quantum computers get scaled up and stabilized, traditional cryptographic systems are one step closer to being obsolete, necessitating the development of robust and future-proof alternatives. This chapter investigates the landscape of quantum-based algorithms and protocols, with a focus on their applicability to the Internet of Things (IoT) ecosystem, ranging from low-power edge sensors to more capable embedded systems. The theoretical basis and practical applications of Quantum Resistant Cryptography (QRC) and Quantum Key Distribution (QKD) are analyzed, examining their computational requirements, energy consumption, scalability, and integration possibilities in IoT architectures with limited resources. In particular, how various Post-Quantum Cryptography (PQC) schemes, such as lattice-based, code-based, and hash-based cryptography, perform across different classes of IoT hardware is discussed. The chapter further investigates ongoing standardization efforts, implementation obstacles, and innovative solutions specifically designed for heterogeneous IoT environments. Moreover, the feasibility of QKD in resource-constrained scenarios is examined, including low-power QKD implementations for embedded and edge devices in IoT networks. Also, the trade-offs between security and efficiency are discussed, considering real-world deployment scenarios and resource constraints. Furthermore, a comprehensive threat model is presented, and the security of current literature is analyzed based on this model. By combining insights from recent literature, a comprehensive understanding of how quantum-based security methodologies can be integrated across the IoT spectrum is provided to guarantee long-term security resilience in the era of quantum computing. This chapter aims to serve as a foundational reference for researchers and practitioners seeking to build quantum-resistant or quantum-enabled IoT infrastructures.