The centrosome is an evolutionarily conserved, ancient organelle whose role in cell division was first described over a century ago. The structure and function of the centrosome as a microtubule-organizing center, and of its extracellular extension – the primary cilium – as a sensory antenna, have since been extensively studied, but the role of the cilium–centrosome axis in cell fate is still emerging. In this Opinion piece, we view cellular quiescence and tissue homeostasis from the vantage point of the cilium–centrosome axis. We focus on a less explored role in the choice between distinct forms of mitotic arrest – reversible quiescence and terminal differentiation, which play distinct roles in tissue homeostasis. We outline evidence implicating the centrosome–basal body switch in stem cell function, including how the cilium–centrosome complex regulates reversible versus irreversible arrest in adult skeletal muscle progenitors. We then highlight exciting new findings in other quiescent cell types that suggest signal-dependent coupling of nuclear and cytoplasmic events to the centrosome–basal body switch. Finally, we propose a framework for involvement of this axis in mitotically inactive cells and identify future avenues for understanding how the cilium–centrosome axis impacts central decisions in tissue homeostasis.