Cognitive neuroscience set out to understand the neural mechanisms underlying cognition. One central question is how oscillatory brain activity relates to cognitive processes. Up to now, most of the evidence supporting this relationship was correlative in nature. This situation changed dramatically with the recent development of non-invasive brain stimulation (NIBS) techniques, which open up new vistas for neuroscience by allowing researchers for the first time to validate their correlational theories by manipulating brain functioning directly. In this review, we focus on transcranial alternating current stimulation (tACS), an electrical brain stimulation method that applies sinusoidal currents to the intact scalp of human individuals to directly interfere with ongoing brain oscillations. We outline how tACS can impact human brain oscillations by employing different levels of observation from non-invasive tACS application in healthy volunteers and intracranial recordings in patients to animal studies demonstrating the effectiveness of alternating electric fields on neurons in vitro and in vivo. These findings likely translate to humans as comparable effects can be observed in human and animal studies. Neural entrainment and plasticity are suggested to mediate the behavioral effects of tACS. Furthermore, we focus on mechanistic theories about the relationship between certain cognitive functions and specific parameters of brain oscillaitons such as its amplitude, frequency, phase and phase coherence. For each of these parameters we present the current state of testing its functional relevance by means of tACS. Recent developments in the field of tACS are outlined which include the stimulation with physiologically inspired non-sinusoidal waveforms, stimulation protocols which allow for the observation of online-effects, and closed loop applications of tACS.