Traditional and lightweight cryptography primitives and protocols are insecure against quantum attacks. Thus, a real-time application using traditional or lightweight cryptography primitives and protocols does not ensure full-proof security. Post-quantum Cryptography is important for the Internet of Things (IoT) due to its security against Quantum attacks. This paper offers a broad literature analysis of post-quantum cryptography for IoT networks, including the challenges and research directions to adopt in real-time applications. The work draws focus towards post-quantum cryptosystems that are useful for resource-constraint devices. Further, those quantum attacks are surveyed, which may occur over traditional and lightweight cryptographic primitives.