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The argument that active galaxies and quasars are powered by accretion onto massive compact objects was first made almost four decades ago (Salpeter 1964; Zeldovich 1964). Since that time, the existence of supermassive black holes has been confirmed in the nuclei of nearby galaxies and in a handful of more distant galaxies by direct dynamical measurement of their masses. The best determinations are in our own Galaxy (Mbullet approx 3 × 106 Msun, Genzel et al. 2000; Ghez et al. 1998), NGC 4258 (Miyoshi et al. 1995), and M87 (Macchetto et al. 1997). The data for each of these galaxies exhibit a clear rise very near the center in the orbital velocity of stars or gas, suggestive of motion around a compact object. Data of this quality are unfortunately still rare, and the majority of black hole detections have necessarily been based on stellar-kinematical data which do not exhibit a clear signature of the presence of a black hole. These data (Magorrian et al. 1998; Richstone et al. 1998) imply a mean black hole mass that is uncomfortably large compared with values predicted from quasar light. The inconsistency has been taken as evidence for low radiative efficiencies during the optically bright phase of quasars (e.g. Haehnelt, Natarajan & Rees 1998) or for continued growth of black holes after the quasar epoch (e.g. Richstone et al. 1998).

It is now clear that this discrepancy was due almost entirely to systematic errors in the stellar kinematical mass estimates. The first convincing demonstration of this came from the Mbullet - sigma relation, a tight empirical correlation between black hole mass and bulge velocity dispersion. The Mbullet - sigma relation was discovered by ranking black hole detections in terms of their believability and excluding the least secure cases. The remarkable and unexpected result (Ferrarese & Merritt 2000) was an almost perfect correlation between Mbullet and sigma for the best-determined black hole masses, compared to a much weaker correlation for the less secure masses. Ground-based, stellar kinematical estimates of Mbullet were found to scatter above the Mbullet - sigma relation by as much as two orders of magnitude, suggesting that many of the published masses were spurious and that most were substantial overestimates.

The ability of the Mbullet - sigma relation to "separate the wheat from the chaff" has led to a rapid advance in our understanding of black hole demographics. We review that progress in Section 2 and Section 3; we argue that there is now almost embarrassingly good agreement between the results from the various techniques for estimating the mean mass density of black holes in the universe. Black hole masses determined dynamically in nearby quiescent galaxies are now fully consistent with masses inferred in active galaxies and quasars, and with estimates of the density of dark relic objects produced by accretion during the quasar epoch. The need for non-standard accretion histories in order to reproduce a large density of black holes in the current universe has disappeared.

Two recurrent themes in this review are the importance of adequate data when estimating black hole masses; and the much greater usefulness of accurate mass estimates compared with simple detections. When the first black hole detections were being published, there was much discussion about whether the observations (all ground-based at the time) were of sufficient quality to resolve the black holes' sphere of influence, rh = GMbullet / sigma2. We now know that the ground-based data almost always failed to do this, sometimes by a large factor, and that this failure, coupled with shortcomings in the modelling, led to systematic overestimates of Mbullet (Section 2). The situation has improved somewhat with the Space Telescope, but not dramatically: we argue (Section 4) that the number of galaxies with secure dynamical estimates of Mbullet will increase only modestly over the next few years in spite of ambitious ongoing programs with HST. This is due partly to the fact that these observations were planned at a time when the mean black hole mass was believed to be much larger than it is now. Progress in our understanding of black hole demographics is more likely to come from techniques with higher effective resolution than stellar or gas kinematics, notably reverberation mapping in AGN (Peterson 1993).

While the ability of the Mbullet - sigma relation to clarify the data has been an enormous boon, the existence of such a tight correlation must also be telling us something fundamental about the way in which black holes form and about the connection between black holes and bulges. Unfortunately, the theoretical understanding of this connection has lagged behind the phenomenology. We summarize the proposed explanations for the origin of the Mbullet - sigma relation in Section 5 and discuss their strengths and weaknesses.

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