High spatial-resolution measurements of surface brightness fluctuations (SBFs) with the Hubble Space Telescope (HST) provide the most precise distances available to early-type galaxies beyond the Local Group. The observable SBF magnitude in a given bandpass is a basic property of any stellar system, corresponding to a ratio of the first and second moments of the stellar luminosity function. Calibration of the method has presented challenges, but we now have an excellent empirical determination of how the SBF observable varies with galaxy color in broad bandpasses at the red end of the optical spectrum, and we are working towards a similar calibration for HST's Wide-Field Camera 3 in the near-infrared wavelength range, where the SBF magnitudes are considerably brighter. From HST Advanced Camera for Surveys data, we have determined the relative distances of the Virgo and Fornax clusters to within a precision of 2%, and resolved their internal structures. More recent measurements allow us to tie the Coma cluster, the standard of comparison for distant cluster studies, to the same precise distance scale. The SBF method can be calibrated in an absolute sense either empirically using Cepheids or theoretically based on stellar population models. The agreement between model and empirical zero points provides an independent confirmation of the Cepheid distance scale.