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Much research has been performed investigating the challenging issue of efficiently utilizing the network-wide capacity available in the multihop wireless mesh networks with multiple radios and multiple channels. In this work, multihop routing and channel assignment are intertwined issues. In this article we present summaries of this work based on two broad categorizations in terms of algorithm features: centralized and distributed approaches. Due to the multiple dimensions of the topics, we subgroup the papers in terms of how the interactions between routing and channel assignments are treated. They include channel assignment based on the given connectivity graph, joint design of routing and channel assignment, routing with localized considerations on channel selection, and channel assignment with local channel usage and traffic load information. With the centralized approach, the schemes are able to target optimal channel assignment and joint design on both channel assignment and routing issues. In the distributed approach, the papers take steps focused on either route metrics or channel scheduling based on localized information about the links at each node. Comparisons and open research issues are given as the conclusion.