The nondominant hemisphere (usually the right) is responsible for primary cognitive functions such as visuospatial and social cognition. Awake surgery using direct electric stimulation for right cerebral tumor removal remains challenging because of the complexity of the functional anatomy and difficulties in adapting standard bedside tasks to awake surgery conditions. An understanding of semiology and anatomic bases, along with an analysis of the available cognitive tasks for visuospatial and social cognition per operative mapping allow neurosurgeons to better appreciate the functional anatomy of the right hemisphere and its relevance to tumor surgery. In this article, the first of a 2-part review, we discuss the anatomic and functional basis of right hemisphere function. Whereas part II of the review focuses primarily on semiology and surgical management of right-sided tumors under awake conditions, this article provides a comprehensive review of knowledge underpinning awake surgery on the right hemisphere.