Surveys of galaxy clusters provide a sensitive probe of cosmology by measuring the evolution of the halo mass function. However, already current cluster surveys are systematically limited by uncertainties in the relation between cluster mass and observables (e.g. X-ray luminosity, cluster richness, SZ decrement). Cluster weak lensing is the most promising observational method to calibrate the mass scaling to the needed precision, but requires the control of systematic errors to a few percent each.  I will discuss the "Weighing the Giants” (WtG) project, which carefully investigated and quantified all sources of systematic uncertainty, resulting in accurate weak lensing masses for 51 clusters.  From a sample of ~200 clusters selected from the ROSAT All-Sky Survey, WtG places some of the tightest constraints on a number of cosmological parameters, including the dark energy equation of state, neutrino masses, and modified gravity.  Furthermore, when adopting the WtG mass calibration, the results from Planck CMB temperature anisotropies and Planck cluster counts are consistent without invoking the need for new physics.  These results bode extremely well for future cluster surveys which will be able to utilize LSST's weak lensing capabilities to anchor the cluster mass scale.