Animals can predict the time of occurrence of a forthcoming event relative to a preceding stimulus, i.e. the interval time between those two, given previous learning experience with the temporal contingency between them. Accumulating evidence suggests that a particular pattern of neural activity observed during tasks involving fixed temporal intervals might carry interval time information: the activity of some cortical and subcortical neurons ramps up slowly and linearly during the interval, like a temporal integrator, and peaks around the time at which the event is due to occur. The slope of this climbing activity, and hence the peak time, adjusts to the length of a temporal interval during repetitive experience with it. Various neural mechanisms for producing climbing activity with variable slopes, representing the length of learned intervals, are discussed.