Caffeine can alleviate headaches caused by caffeine withdrawal due to its dual role as both a vasodilator and vasoconstrictor. By blocking adenosine receptors, caffeine prevents sleepiness and can induce vasoconstriction when adenosine levels are high. However, when well-rested, caffeine may promote vasodilation, highlighting the complex effects of caffeine on our bodies depending on our state of alertness and rest.