Research papers in lightweight authentication for the Constrained Application Protocol (CoAP) explore solutions to ensure secure identity verification and message integrity in IoT environments while keeping computational and communication overhead to a minimum. Since CoAP is designed for resource-constrained devices operating in Low-Power and Lossy Networks (LLNs), traditional authentication protocols such as TLS/DTLS are often unsuitable due to their high handshake latency, memory footprint, and energy consumption. To overcome these challenges, researchers have proposed lightweight authentication mechanisms that use symmetric key cryptography, elliptic curve cryptography (ECC), identity-based authentication, and certificate-less schemes. Symmetric key-based methods rely on pre-shared keys (PSK) and message authentication codes (MACs) to provide fast and low-cost authentication, though scalability and key distribution remain challenges. ECC-based approaches, particularly ECDH and ECDSA, are widely studied for CoAP due to their strong security with smaller key sizes, offering a balance between lightweight operation and robustness. Identity-based and certificate-less authentication schemes reduce the burden of managing digital certificates, making them attractive for constrained IoT scenarios. At the application layer, Object Security for Constrained RESTful Environments (OSCORE) provides end-to-end authentication and integrity protection for CoAP messages with low overhead, while group-based authentication mechanisms are explored for multicast communication. Several works also propose proxy-assisted authentication, blockchain-based trust management, and context-aware lightweight authentication protocols to enhance scalability and adaptability. More recent approaches integrate lightweight authentication with intrusion detection, machine learning, and cross-layer optimization to provide adaptive and resilient security against spoofing, replay, and man-in-the-middle attacks. Despite these advancements, open issues remain in terms of defending against insider threats, ensuring fairness in group authentication, achieving scalability in large deployments, and designing ultra-lightweight mechanisms without compromising security guarantees. Overall, the literature shows that lightweight authentication is an essential component for securing CoAP-based IoT systems, and ongoing research continues to balance strong security with the severe resource limitations of constrained devices.