Wireless mesh networks are a special type of broadcast networks which cover the qualifications of both ad-hoc as well as infrastructure mode networks. These networks offer connectivity to the last mile through hop to hop communication and by comparatively reducing the cost of infrastructure in terms of wire and hardware. Channel assignment has always been the focused area for such networks specifically when using non-overlapping channels and sharing radio frequency spectrum while using multiple radios. It has always been a challenge for mesh network on impartial utilization of the resources (channels), with the increase in users. The rational utilization of multiple channels and multiple radios, not only increases the overall throughput, capacity and scalability, but also creates significant complexities for channel assignment methods. For a better understanding of research challenges, this paper discusses heuristic methods, measurements and channel utilization applications and also examines various researches that yield to overcome this problem. Finally, we highlight prospective directions of research.