This and two companion papers (Geography and the Anthropocene II: Current Contributions and The Anthropocene and Geography III: Future Directions) consider the relevance of 'the Anthropocene' to present and future research in Geography. Along with the concept of 'planetary boundaries', the idea that humanity has entered a new geological epoch of its own making is currently attracting considerable attention - both within and beyond the world of Earth surface science from whence both notions originate. This paper summarises the origins and evolution of the scientific discourse since the Anthropocene idea was first proposed in 2000. It ends by outlining the potential relevance of the Anthropocene and planetary boundaries ideas to Geography - potential because both concepts have only recently received serious attention in the discipline. The next paper, following on from this, then reviews these early geographical interpretations of the two scientific buzzwords. The subsequent paper looks ahead to future options should these terms really begin to catch-on outside Geography. If they become societal keywords, then geographers should be participants in, rather than mere observers of, the unfolding discussion. As we will discover, some geographers are well-placed to shape future discourse and practice, but there is considerable potential for many others to join the fray.