Abstract: The Virasoro-Shapiro amplitude on AdS5xS5 is the full tree-level string amplitude of four gravitons on AdS5xS5, or the four-point correlator of the stress-energy tensor in planar N=4 SYM including all order corrections in $1/\lambda$. In this talk I will explain how this correlator can be determined using target space considerations, similar to the ones that led to the discovery of the Veneziano amplitude. Boundedness in the Regge limit follows from the bound on chaos and lets us derive dispersive sum rules that relate the Wilson coefficients from the low energy effective action with the OPE data of short massive operators in N=4 SYM theory at strong coupling. For the first curvature correction we found a unique solution to the dispersive sum rules which has a representation as a world-sheet integral over the Riemann sphere. This solution reproduces all localisation results for Wilson coefficients and all CFT data available from integrability and produces a wealth of new CFT data for planar N=4 SYM at strong coupling.