Caveolae are small coated plasma membrane invaginations with diverse functions. Caveolae undergo curvature changes. Yet, it is unclear which proteins regulate this process. To address this gap, we develop a correlative stimulated emission depletion (STED) fluorescence and platinum replica electron microscopy imaging (CLEM) method to image proteins at single caveolae. Caveolins and cavins are found at all caveolae, independent of curvature. EHD2 is detected at both low and highly curved caveolae. Pacsin2 associates with low curved caveolae and EHBP1 with mostly highly curved caveolae. Dynamin is absent from caveolae. Cells lacking dynamin show no substantial changes to caveolae, suggesting that dynamin is not directly involved in caveolae curvature. We propose a model where caveolins, cavins, and EHD2 assemble as a cohesive structural unit regulated by intermittent associations with pacsin2 and EHBP1. These coats can flatten and curve to enable lipid traffic, signaling, and changes to the surface area of the cell.