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Transcranial alternating current stimulation (tACS) is a non-invasive brain stimulation technique that allows the manipulation of intrinsic brain oscillations. Numerous studies have applied tACS in the laboratory to enhance cognitive performance. With this systematic review, we aim to provide an overview of frequency-specific tACS effects on a range of cognitive functions in healthy adults. This may help to transfer stimulation protocols to real-world applications. We conducted a systematic literature search on PubMed and Cochrane databases and considered tACS studies in healthy adults (age > 18 years) that focused on cognitive performance. The search yielded n = 109 studies, of which n = 57 met the inclusion criteria. The results indicate that theta-tACS was beneficial for several cognitive functions, including working memory, executive functions, and declarative memory. Gamma-tACS enhanced performance in both auditory and visual perception but it did not change performance in tasks of executive functions. For attention, the results were less consistent but point to an improvement in performance with alpha- or gamma-tACS. We discuss these findings and point to important considerations that would precede a transfer to real-world applications.