Abstract: One of the great surprises to emerge from string theory is the prediction of supersymmetric QFTs with interacting UV superconformal fixed points in 5d and 6d. Although 6d superconformal fixed points are believed classified, the classification of 5d superconformal fixed points remains an open problem. In this talk, I discuss recent progress towards a classification of 5d fixed points in terms of singular Calabi-Yau 3-folds. I will also explain how families of RG flows between different 5d fixed points are encoded in geometry, how these RG flows establish a direct connection with 6d fixed points, and how this connection can be made into a systematic classification program.