Physics education research (PER) is a relatively new and rapidly growing area of Ph.D. specialization. To sustain the field of PER, a steady pipeline of talented scholars needs to be developed and supported. One aspect of building this pipeline is understanding how students come to graduate and postdoctoral work in PER and what their career goals are. This paper presents the first study on the experiences and career pathways of students in PER. Data were collected through open-ended interviews with 13 graduate students and postdoctoral scholars in PER. Results show that many of these PER graduate students and postdoctoral scholars were not aware of PER as undergraduates. PER graduate students that were aware of PER as undergraduates chose to study PER as they were applying to graduate schools. The graduate school experiences of the interviewees were overwhelmingly positive, with participants reporting a positive climate that was facilitated by communicative and productive relationships with their advisors. However, some participants reported concerns about the acceptance of PER within some departments, including open hostility towards the field. The majority of participants were interested in pursuing a career as a university faculty member, with more participants preferring a position at a research-intensive university. These results suggest that a further large-scale study of graduate students in PER may be able to highlight the field as being a leader in student mentoring and community development while collecting important demographic information that could show PER to have more gender diversity than other subfields of physics. (Contains 4 tables.)