I will present results based on high resolution CO maps from the PHANGS-ALMA to estimate the star formation efficiency per gravitational free-fall time, SFEff, at the scale of giant molecular clouds. PHANGS-ALMA allows us to make these measurements across a representative sample of 70 nearby galaxies, making this by far the largest measurement to date of this key quantity. I will show that SFEff is on the order of 1%, consistent with some theoretical expectations, but with significant variation from galaxy-to-galaxy and between regions inside a galaxy. I will explain how these variations correlate with host galaxy properties, in the sense that SFEff anti-correlates with the total stellar mass and the molecular-to-total gas mass ratio. I will also compare SFEff to the local (100 pc) structural properties of the molecular gas. SFEff shows a strong anti-correlation with local molecular gas mass surface density and velocity dispersion, but only a weak relationship with the virial parameter. These trends are not trivially reproduced by current models of star formation that are based on a lognormal distribution of gas density.