This article examined the state-of-the-art overview of the most relevant routing protocols that have been proposed as part of constrained networks, including Wireless Sensor Networks (WSNs) and the Internet of Things (IoTs). This category of network will be one of the main parts of the future global network. Therefore, achieving satisfactory performance on constrained networks is a current research challenge, especially at the routing level. In this vision, the classification of routing protocols in sensor networks is established and the current state of standardization in the area of the Internet of Things is updated. In addition, a comparison of the described protocols is discussed for each class of algorithms. Finally, some technological challenges and some emerging lines of recent research on resource-constrained routing approaches for WSNs and IoTs are briefly discussed.