Brain imaging is based on measuring not neural activity but rather, brain hemodynamics – local changes in blood volume, blood flow and oxygenation. These hemodynamic signals are understood to reliably report local neural activity. In particular, it is typically assumed that the hemodynamics follow uniformly from local neural responses, with increases in neural activity causing local deoxygenation in the blood which then drives fresh oxygenated blood into the activated regions of the brain. However, the neurophysiology of brain imaging has primarily been studied in anesthetized animals. Neural and hemodynamic responses have rarely been compared in alert subjects to understand how these signals relate to each other in individuals engaged in a behavioral task. By recording with electrodes while simultaneously imaging hemodynamic signals in alert behaving monkeys, we find a complex relationship between hemodynamics and neural activity. This complexity is evident at two levels. First we find that when the animals are engaged in a systematic visual task, the hemodynamic signal recorded from their primary visual cortex (V1) contains a strong task-related component in addition to visually evoked responses. This task-related component is a novel anticipatory signal that dilates local arteries and brings in fresh blood ahead of an expected visual trial. Unlike the visually driven signal, this task-related component is independent of visual input or measurable local neural activity, whether spiking or local field potential (LFP). We speculate that this task-related signal may result from distal neuromodulatory inputs into visual cortex. Next, we find that even the visually evoked hemodynamic signal is not driven by deoxygenation in the blood per se. Rather, it is likely driven by a process that occurs in parallel, roughly anticipating the local demand before it leads to any blood deoxygenation. These findings should lead to a better appreciation both of the multiple neural mechanisms underlying brain hemodynamics and the causal relationships linking neural activity and blood flow.