It can be convenient to think of the genome as simply a string of nucleotides, the linear order of which encodes an organism's genetic blueprint. However, the genome does not exist as a linear entity within cells where this blueprint is actually utilized. Inside the nucleus, the genome is organized in three-dimensional (3D) space, and lineage-specific transcriptional programs that direct stem cell fate are implemented in this native 3D context. Here, we review principles of 3D genome organization in mammalian cells. We focus on the emerging relationship between genome organization and lineage-specific transcriptional regulation, which we argue are inextricably linked.