Through neuromodulation of neural activity, transcranial alternating current stimulation (tACS) interacts with neural oscillations in a frequency- and phase-specific manner, thereby influencing human brain function. Currents are applied at the scalp with intensities up to 4 mA peak to peak (except for electroconvulsive therapy with much higher intensities), for minutes and rarely hours/day. Possible physical variations of the stimulation spectrum are indefinite, transcranial random noise stimulation (tRNS) representing a simple example. Animal experiments have demonstrated in what way neurons react to invasively and transcranially applied alternating currents. Such findings, supported by modelling studies, studies on human physiology and behaviour, invasive stimulation and recording from epilepsy patients helped to understand how we can entrain oscillations in the human brain. In future, the methods might increasingly be applicable in the therapy of disorders with malfunctioning brain oscillations.