Research papers in lightweight authentication for the MQTT (Message Queuing Telemetry Transport) protocol focus on enabling secure client-broker interactions in IoT networks while minimizing computational, communication, and energy overhead on constrained devices. MQTT, being a lightweight publish-subscribe protocol designed for low-bandwidth and high-latency networks, does not include built-in robust authentication mechanisms, making it vulnerable to spoofing, replay, and unauthorized access attacks. To address these challenges, researchers have proposed various lightweight authentication schemes. Symmetric key-based methods using pre-shared keys (PSK) and message authentication codes (MACs) provide fast and low-overhead authentication, although scalability and secure key distribution remain critical concerns. Elliptic Curve Cryptography (ECC)-based approaches, including ECDH and ECDSA, are widely studied for secure authentication and integrity verification due to smaller key sizes and lower computational cost compared to traditional public-key cryptography. Identity-based and certificate-less authentication schemes are explored to simplify key management in large-scale MQTT deployments. Application-layer solutions, such as token-based authentication, OAuth 2.0 adaptations, and integration with lightweight security frameworks, provide additional flexibility and security. Some studies also combine lightweight authentication with trust-based models, intrusion detection, and blockchain-assisted mechanisms to enhance resilience against malicious nodes and insider attacks. Recent works emphasize adaptive and context-aware authentication schemes that balance security with energy efficiency, latency, and scalability in IoT deployments. Despite advancements, challenges remain in ensuring group authentication, defending against collusion or insider threats, and designing ultra-lightweight protocols suitable for dense and heterogeneous MQTT networks. Overall, the literature highlights that lightweight authentication is a crucial component for securing MQTT-based IoT systems, enabling reliable and trusted communication without overburdening resource-constrained devices.