Abstract: On the basis of measurements of superfluid density NS and transition temperatures Tc, we argue that the physics of underdoped cuprates is dominated by fluctuations associated with a quantum superconductor-to-insulator phase transition. "Thick" films exhibit 3D scaling of Tc with NS, while ultrathin films two unit cells thick exhibit the expected 2D scaling. Observation of 3D fluctuations contradicts the well-known "Uemura relation" which holds that thick samples have 2D fluctuations. On the other side of the cuprate phase diagram, recent results on overdoped La2-xSrxCuO4 films show that these films suddenly become amazingly homogeneous, possibly due to another quantum phase transition. We'll speculate on what might be going on there.