Crossbar circuitry, and a method of operation of such crossbar circuitry, are provided. The crossbar circuitry has an array of data input paths and data output paths where the data output paths are transverse to the data input paths. At each intersection between a data input path and a data output path, a crossbar cell is provided that comprises a configuration storage circuit programmable to store a routing value, a transmission circuit, and an arbitration circuit. In a transmission mode of operation, the transmission circuit is responsive to the routing value being a first value, indicating that the data input path should be coupled to the data output path, to detect the data input along the data input path, and to output an indication of that data on the data output path at the associated intersection. In an arbitration mode of operation, the arbitration circuitry is operable in the presence of an asserted transmission request from the associated source circuit to operate in combination with the arbitration circuits of other crossbar cells associated with the same data output path to re-use the bit lines of the data output path to detect the presence of multiple asserted transmission requests for the same data output path. In the event of such multiple asserted transmission requests, the arbitration circuitry operates in combination with the other arbitration circuits to implement a predetermined priority scheme to cause the configuration storage circuit of only one crossbar cell associated with the same data output path to have its routing value programmed to the first value, thereby resolving conflict between the multiple asserted transmission requests according to the predetermined priority scheme. Such a construction of crossbar circuitry enables a very efficient resolution of conflicts to be performed, whilst providing a very regular design, with uniform delay across all paths, and which requires significantly less control lines that typical prior art crossbar designs. Such crossbar circuitry is readily scalable to form large crossbars.