Intraoperative language and sensorimotor function mapping with direct electrical stimulation allows precise identification of functionally important brain regions. Direct electrical stimulation brain mapping has become the standard of care for the resection of brain lesions near or within eloquent regions with various patient outcome benefits. Intraoperative stimulation mapping (ISM) is commonly performed in an awake patient for language and motor assessments. However, motor mapping under general anesthesia, termed asleep motor mapping, has been increasingly performed over the last two decades for lesions primarily affecting the motor areas of the brain. Both asleep-awake-asleep and monitored anesthesia care have been successfully used for awake craniotomy in modern neuroanesthesia. Each anesthetic agent exerts varying effects on the quality of ISM, especially under general anesthesia. Careful selection of an anesthetic technique is crucial for the successful performance of ISM in both awake and asleep conditions. A comprehensive search was performed on electronic databases such as PubMed, Embase, Cochrane, Scopus, Web of Science, and Google Scholar to identify articles describing anesthesia for awake craniotomy, intraoperative brain mapping, and asleep motor mapping. In the second part of this narrative review, we summarize the effects of different anesthetic regimes and agents on ISM, causes of the failure of awake craniotomy and mapping, and outline the anesthetic considerations for ISM during awake craniotomy and asleep motor mapping.