The rapid expansion of the Internet of Things (IoT) has led to a significant increase in connected devices, resulting in growing challenges related to efficient data transmission, energy consumption, and network scalability. Routing protocols and energy-efficient algorithms play a pivotal role in addressing these challenges, enabling IoT systems to optimize performance while minimizing power usage. This review provides a comprehensive analysis of recent advancements in IoT routing techniques and energy-efficient solutions, focusing on multi-objective optimization algorithms such as fractional gravitational search, grey wolf optimization, and hybrid salp swarm-differential evolution algorithms. Additionally, we explore context-aware routing, cluster-based methods, and the integration of machine learning to enhance decision-making in dynamic IoT environments. The review also highlights the critical role of energy-efficient routing in IoT applications, such as smart agriculture, healthcare, and smart cities, emphasizing its importance in prolonging network lifetime and reducing overall operational costs. The potential of blockchain technology and AI-driven algorithms to enhance security and energy efficiency in IoT networks is discussed, alongside future directions in green routing solutions. By addressing the complexities of IoT routing and energy management, this review aims to provide insights into the latest research trends and guide future innovations in IoT systems.