A brief overview of the methods commonly used to determine or estimate the black-hole mass in quiescent or active galaxies is presented and it is argued that the use of mass-scaling relations is both a reliable and the preferred method to apply to large samples of distant quasars. The method uses spectroscopic measurements of a broad emission-line width and continuum luminosity and currently has a statistical 1σ uncertainty in the absolute mass values of about a factor of 4. Potentially, this accuracy can be improved in the future. When applied to large samples of distant quasars it is evident that the black-hole masses are very large, of order 1 to 10 billion M⊙, even at the highest redshifts of 4 to 6. The black holes must build up their mass very fast in the early universe. Yet they do not grow much larger than that: a maximum mass of ~1010M⊙ is also observed. Preliminary mass functions of active black holes are presented for several quasar samples, including the Sloan Digital Sky Survey. Finally, common concerns related to the application of the mass-scaling relations, especially for high redshift quasars, are briefly discussed.