Witten (91) defined an intersection theory on the moduli spaces of closed Riemann surfaces with r-spin structures. I will explain how to construct, using a technique called 'point insertion', an intersection theory for holomorphic disks with r-spin structures. This generalizes the previous construction by Buryak-Clader-Tessler and allows us to define more general open Fan-Jarvis-Ruan-Witten theories. If time permits, I will talk about the construction of the intersection theory for cylinders with r-spin structures. Based on joint works with R. Tessler.