Brain oscillations of different frequencies have been associated with a variety of cognitive functions. Convincing evidence supporting those associations has been provided by studies using intracranial stimulation, pharmacological interventions and lesion studies. The emergence of novel non-invasive brain stimulation techniques like repetitive transcranial magnetic stimulation (rTMS) and transcranial alternating current stimulation (tACS) now allows to modulate brain oscillations directly. Particularly, tACS offers the unique opportunity to causally link brain oscillations of a specific frequency range to cognitive processes, because it uses sinusoidal currents that are bound to one frequency only. Using tACS allows to modulate brain oscillations and in turn to influence cognitive processes, thereby demonstrating the causal link between the two. Here, we review findings about the physiological mechanism of tACS and studies that have used tACS to modulate basic motor and sensory processes as well as higher cognitive processes like memory, ambiguous perception, and decision making.