Multi-hop, multi-channel, and multi-radio wireless mesh networks (WMNs) are emerging as promising field of wireless technology with self-organizing and self-healing features for internet and real time applications, i.e., VoIP and Video over IP. Interoperability feature of WMNs have made them to integrate easily with other network technologies like wired networks, WiFi, WiMax, MANETs, and cellular networks. WMNs are gaining popularity due to their high network throughput which highly depends on the routing procedures. Routing algorithms like optimized link state routing protocol and dynamic source routing make efficient routing decisions on the basis of routing metrics which actually predict the cost of link quality. Most of the routing protocols and routing metrics implemented in WMNs are actually designed for mobile ad hoc networks (MANETs). Since WMNs have different characteristics and limitations as compared to MANETs, so the routing metrics design for MANETs do not perform well in WMNs. Furthermore, quality of service (QoS) and throughput of the network in WMNs can be enhanced by using cross layer routing approach and by deploying multi-channel multi-radio (MCMR) scenarios in each relay node. This article discusses a design taxonomy, limitations and qualitative comparison of existing routing metrics for QoS in MCMR WMNs with respect to routing parameters, i.e., transmission rate, inter-flow interference, intra-flow interference, congestion, and channel diversity. Moreover, our taxonomy also opens the door up for new research areas in the design of cross layer routing metrics for MCMR radio WMNs for high throughput IP connectivity.