This paper presents a methodological framework for developing scientific mobility indicators based on bibliometric data. We identify nearly 16 million individual authors from publications covered in the Web of Science for the 2008–2015 period. Based on the information provided across individuals’ publication records, we propose a general classification for analyzing scientific mobility using institutional affiliation changes. We distinguish between migrants–authors who have ruptures with their country of origin–and travelers–authors who gain additional affiliations while maintaining affiliation with their country of origin. We find that 3.7% of researchers who have published at least one paper over the period are mobile. Travelers represent 72.7% of all mobile scholars, but migrants have higher scientific impact. We apply this classification at the country level, expanding the classification to incorporate the directionality of scientists’ mobility (i.e., incoming and outgoing). We provide a brief analysis to highlight the utility of the proposed taxonomy to study scholarly mobility and discuss the implications for science policy.