A common criticism of the current Internet is the fact that it does not offer quality of service (QoS) guarantees across autonomous system boundaries. The Border Gateway Protocol (BGP) is central to solve this problem, since it enables AS to distribute reachability information. However, BGP is agnostic of any performance or QoS metrics. For this reason, the debate about the requirements for the future interdomain routing architecture and about whether these requirements are best met by an approach of introducing changes into BGP or by replacing BGP is still open. This article provides an insight into the interdomain QoS routing problem. First, the main drawbacks of current interdomain routing with regard to the provision of QoS are identified. Second, a survey of the most relevant interdomain QoS routing approaches are described and discussed. We also give a broad perspective on challenges surrounding the issue of whether to extend or replace BGP to support QoS, with particular emphasis on the technical challenges. However, we also point out some nontechnical unsolved challenges