Sleep helps to consolidate previously acquired memories. Whether new information such as languages and other useful skills can also be learned during sleep has been debated for over a century, however, the sporadic studies' different objectives and varied methodologies make it difficult to draw definitive conclusions. This review provides a comprehensive overview of the history of sleep learning research conducted in humans, from its empirical beginnings in the 1940s to the present day. Synthesizing the findings from 51 research papers, we show that several studies support the notion that simpler forms of learning, such as habituation and conditioning, are possible during sleep. In contrast, the findings for more complex, applied learning (e.g., learning a new language during sleep) are more divergent. While there is often an indication of processing and learning during sleep when looking at neural markers, behavioral evidence for the transfer of new knowledge to wake remains inconclusive. We close by critically examining the limitations and assumptions that have contributed to the discrepancies in the literature and highlight promising new directions in the field.