Centrosomes are self-assembling, micron-scale, nonmembrane bound organelles that nucleate microtubules (MTs) and organize the microtubule cytoskeleton of the cell. They orchestrate critical cellular processes such as ciliary-based motility, vesicle trafficking, and cell division. Much is known about the role of the centrosome in these contexts, but we have a less comprehensive understanding of how the centrosome assembles and generates microtubules. Studies over the past 10 years have fundamentally shifted our view of these processes. Subdiffraction imaging has probed the amorphous haze of material surrounding the core of the centrosome revealing a complex, hierarchically organized structure whose composition and size changes profoundly during the transition from interphase to mitosis. New biophysical insights into protein phase transitions, where a diffuse protein spontaneously separates into a locally concentrated, nonmembrane bounded compartment, have provided a fresh perspective into how the centrosome might rapidly condense from diffuse cytoplasmic components. In this Perspective, we focus on recent findings that identify several centrosomal proteins that undergo phase transitions. We discuss how to reconcile these results with the current model of the underlying organization of proteins in the centrosome. Furthermore, we reflect on how these findings impact our understanding of how the centrosome undergoes self-assembly and promotes MT nucleation.