Centriolar satellites are membraneless granules that localize and move around centrosomes and cilia. Once referred to as structures with no obvious function, research in the past decade has identified satellites as key regulators of a wide range of cellular and organismal processes. Importantly, these studies have revealed a substantial overlap between functions, proteomes, and disease links of satellites with centrosomes and cilia. Therefore, satellites are now accepted as the "third component" of the vertebrate centrosome/cilium complex, which profoundly changes the way we think about the assembly, maintenance, and remodeling of the complex at the cellular and organismal levels. In this perspective, we first provide an overview of the cellular and structural complexities of centriolar satellites. We then describe the progress in the identification of the satellite interactome, which have paved the way to a molecular understanding of their mechanism of action and assembly mechanisms. After exploring current insights into their functions as recently described by loss-of-function studies and comparative evolutionary approaches, we discuss major unanswered questions regarding their functional and compositional diversity and their functions outside centrosomes and cilia.