Within biomedicine, comparative genomics is crucial for interpreting human genetic variants and building proper animal models. As our closest relatives, primates are of particular relevance in this frame work. Here, I review principles and concrete examples of this approach. Since one can expect that generating the necessary genomic DNA sequences will not be the major limiting factor in the near future, I argue that in analogy to human biomedicine, comprehensive phenotyping of different primates will be a crucial next step to tap the full potential of comparative genomics. Especially the possibility to generate pluripotent stem cells from primates should allow extending the comparative approach to many medically relevant questions.