The response of a sensory neuron to an unchanging stimulus typically adapts, showing decreases in response gain that are accompanied by changes in the shape of tuning curves. It remains unclear whether these changes arise purely due to spike rate adaptation within single neurons or whether they are dependent on network interactions between neurons. Further, it is unclear how the timescales of neural and perceptual adaptation are related. To examine this issue, we compared speed tuning of middle temporal (MT) and medial superior temporal neurons in macaque visual cortex after adaptation to two different reference speeds. For 75 of speed-tuned units, adaptation caused significant changes in tuning that could be explained equally well as lateral shifts, vertical gain changes, or both. These tuning changes occurred rapidly, as both neuronal firing rate and Fano factor showed no evidence of changing beyond the first 500 ms after motion onset, and the magnitude of tuning curve changes showed no difference between trials with adaptation durations shorter or longer than 1 s. Importantly, the magnitude of tuning shifts was correlated with the transient-sustained index, which measures a well characterized form of rapid response adaptation in MT, and is likely associated with changes at the level of neuronal networks. Tuning curves changed in a manner that increased neuronal sensitivity around the adapting speed, consistent with improvements in human and macaque psychophysical performance that we observed over the first several hundred ms of adaptation.