The ability of cells to divide, migrate, relay signals, sense mechanical stimuli, and respond to stress all rely on nanoscale invaginations of the plasma membrane known as caveolae. The caveolins, a family of monotopic membrane proteins, form the inner layer of the caveolar coat. Caveolins have long been implicated in the generation of membrane curvature, in addition to serving as scaffolds for signaling proteins. Until recently, however, the molecular architecture of caveolins was unknown, making it impossible to understand how they operate at a mechanistic level. Over the past year, two independent lines of evidence — experimental and computational — have now converged to provide the first-ever glimpse into the structure of the oligomeric caveolin complexes that function as the building blocks of caveolae. Here, we summarize how these discoveries are transforming our understanding of this long-enigmatic protein family and their role in caveolae assembly and function. We present new models inspired by the structure for how caveolins oligomerize, remodel membranes, interact with their binding partners, and reorganize when mutated. Finally, we discuss emerging insights into structural differences among caveolin family members that enable them to support the proper functions of diverse tissues and organisms.