Awake surgery has become a standard practice for managing diffuse low-grade gliomas (LGGs), particularly in eloquent brain areas, and is established as a gold standard technique for left-dominant-hemisphere tumors. However, the intraoperative monitoring of functions in the right non-dominant hemisphere (RndH) is often neglected, highlighting the need for a better understanding of neurocognitive testing for complex functions in the right hemisphere. This article aims to comprehensively review the current literature on the benefits of awake craniotomy in gliomas of the non-dominant right hemisphere. A systematic review was conducted using the PubMed and ScienceDirect databases with keywords such as “right hemisphere”, “awake surgery”, “direct electrical brain stimulation and mapping”, and “glioma”. The search focused on anatomical and surgical aspects, including indications, tools, and techniques of awake surgery in right cerebral hemisphere gliomas. The literature search identified 74 sources, including original articles, books, monographs, and review articles. Two papers reported large series of language assessment cases in 246 patients undergoing awake surgery with detailed neurological semiology and mapping techniques, while the remaining studies were predominantly neuroradiological and neuroimaging in nature. Awake craniotomy for non-dominant-hemisphere gliomas is an essential tool. The term “non-dominant” should be revised, as this hemisphere contributes significantly to essential cognitive functions in the human brain.