As part of a longitudinal study into identity development in upper-level physics students, we used a phenomenographic research method to examine students' perceptions of what it means to be a physicist. Analysis revealed six different categories of perception of what it means to be a physicist. We found the following themes: research and its association with being a physicist, differences in mindset, and exclusivity of accomplishments. The paper highlights how these perceptions relate to two communities of practice that the students are members of, and also highlights the importance of undergraduate research for students to transition from the physics undergraduate community of practice to the community of practicing physicists. [This paper is part of the Focused Collection on Upper Division Physics Courses.]