This brief focuses on the state-of-the-art research for congestion control in Multihop Wireless Networks (MWN), based on the Network Utility Maximization (NUM) framework. The brief evaluates fundamental theories, useful performance investigations, and open issues. Multihop Wireless Networks (MWN), including Ad Hoc networks, Wireless sensor networks, and Wireless Mesh networks, play the essential role in the evolution of pervasive computing. MWN represent complex distributed systems which comprise wireless mobile nodes that can freely and dynamically self-organize into arbitrary and temporary network topology, allowing nodes to seamlessly internetwork in areas with no pre-existing communication infrastructure. "Optimal Utility-based Congestion Control in Multihop Wireless Networks" explores how MWN provide a categorization of applicative scenarios outside of the military domain, such as emergency services, disaster recovery, and environment monitoring.".