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In recent decades, there has been an explosion of data streams spanning the entire spectrum of biomedicine, opening novel opportunities to tackle biological and medical research questions, increasing our ability to provide effective and efficient health care. In parallel, augmented computational power has allowed the development and deployment of quantitative approaches at unprecedented scales. To effectively take advantage of this progress, it is important to invest in the training of a new generation of biomedical data scientists. Designing a graduate curriculum in the backdrop of a rapidly changing landscape of data, methods, and computing power demands flexibility and openness to adaptation. At the same time, we strive to ensure that the students acquire foundational competencies that might fuel productive and evolving careers, without being constrained to and defined by a niche trendy topic. We offer here a view of graduate training in biomedical data science from the standpoint of our experience at Stanford University. We conclude with a series of open challenges, the answers to which we believe will shape training in biomedical data science.