Alterations of cortical excitability, oscillatory as well as non-oscillatory, are physiological derivates of cognitive processes, such as perception, working memory, learning, and long-term memory formation. Since noninvasive electrical brain stimulation is capable of inducing alterations in the human brain, these stimulation approaches might be attractive tools to modulate cognition. Transcranial direct current stimulation (tDCS) alters spontaneous cortical activity, while transcranial alternating current stimulation (tACS) and transcranial random noise stimulation (tRNS) are presumed to induce or interfere with oscillations of cortical networks. Via these mechanisms, the respective stimulation techniques have indeed been shown to modulate cognitive processes in a multitude of studies conducted during the last years. In this review, we will gather knowledge about the potential of noninvasive electrical brain stimulation to study and modify cognitive processes in healthy humans and discuss directions of future research.