Backpressure-based routing and scheduling has been considered as a promising strategy for efficient resource allocation in wireless multihop networks. It has many attractive features such as throughput optimality, achievable adaptive resource allocation, support for agile load-aware routing, and simplicity. In this article, we first categorize existing backpressure-based protocols based on different design criteria and then summarize several key issues faced in the design of efficient backpressure-based protocols. We present a comprehensive survey of state-of-theart backpressure-based protocols for wireless multihop networks. We illustrate how each of the protocols works, and discuss their merits and deficiencies. Finally, we point out some future directions for supporting efficient backpressure- based routing and scheduling.