Contemporary wireless multihop networks operate much below their capacity due to the poor coordination among transmitting nodes. In this paper, we present XPRESS, a cross-layer backpressure architecture designed to reach the capacity of wireless multihop networks. Instead of a collection of poorly coordinated wireless routers, XPRESS turns a mesh network into a wireless switch. Transmissions over the network are scheduled using a throughput-optimal backpressure algorithm. Realizing this theoretical concept entails several challenges, which we identify and address with a cross-layer design and implementation on top of our wireless hardware platform. In contrast to previous work, we implement and evaluate backpressure scheduling over a TDMA MAC protocol, as it was originally proposed in theory. Our experiments in an indoor testbed show that XPRESS can yield up to 128% throughput gains over 802.11.