Software Defined Networking (SDN) is a new approach to configure and manage computer networks, based on its core idea of separating the data plane from the control plane. Through this, SDN provides a higher level of abstraction and allows better and simpler programmability and management of networks, thereby enabling faster innovation. The benefits of SDN have clearly been demonstrated for wired networks, in particular for wide area and data centre networks. The goal of this research was to explore how the concepts of SDN can be applied to wireless networks, in particular Wireless Mesh Networks (WMNs). The focus of our research was on exploring the feasibility of SDN-based routing and load balancing of traffic in WMNs. For this, we leveraged key SDN features such as centralised view of the network state, fine grained and flow-based traffic forwarding, and abstraction. Working towards this goal, we have addressed a number of key research challenges. Firstly, we have designed and implemented a new topology discovery mechanism with greatly reduced overhead compared to the state-of-the-art approach. Topology discovery is an essential service in any Software Defined Network, but an efficient mechanism with low overhead is particularly important for typically resource constrained WMNs. Another critical component for SDN-based routing in WMNs is link monitoring, in particular link capacity monitoring. In contrast to wired networks, where the link capacity is typically known and constant, it can be highly dynamic in wireless networks. We have designed, implemented and evaluated a new, SDN-based link capacity estimation approach, based on the concept of packet pair/train probing. Building on our topology discovery and link capacity estimation methods, we have developed a new SDN-based routing framework for WMNs. For this, we have leveraged a new northbound interface called SCOR (Software-defined Constrained Optimal Routing) for QoS routing and Traffic Engineering (TE). Using the abstraction provided by a small number of high level SCOR routing primitives, we have demonstrated the feasibility, simplicity and efficiency of this approach to implement relatively complex routing problems in WMNs. Finally, we have also provided critical evaluations of new potential testbeds for the evaluation of SDN-based WMNs. We believe this is an important contribution in its own right, since experimental validation is a key research methodology in this context, and trust in the validity of experimental results is absolutely critical.