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We demonstrate dramatic breakdown behavior in the current through GaAs/AlGaAs nanoconstrictions (NCs), and find that this exhibits multiple signatures characteristic of the Gunn effect. These include current fluctuations and hysteresis, and electroluminescence that are consistent with the formation of Gunn domains. An analytical model is developed to describe the current-voltage characteristics of the NCs prior to the onset of the breakdown, and reveals the conduction through them to be barrier limited under low bias. A comparison of the results of these calculations with experiment furthermore suggests that the Gunn effect in these devices is triggered, once the phenomenon of drain-induced barrier lowering becomes sufficiently developed to support the injection of large numbers of electrons into the NC. Our paper, therefore, demonstrates how the Gunn effect may be manipulated through nanoscale tailoring of semiconductors, a result that may have implications for the development of solid-state terahertz technology.