Of all species that have existed on Earth, 99.9 percent are now extinct. Many of them perished in five cataclysmic events.
Even though it's hard to compare past extinction rates with that of the present, given missing data from the past, we do know how to identify extinction periods: the elevation of extinction rates in those periods are at least a hundred-fold over the slow "background" rate of "normal" extinction.
Of about 6 to 10 million currently existing species, we have still only identified 1 million; we know more about vertebrate species than we do about plants and insects. But for groups that we know well, knowledge of very recent species extinctions and for current species, their ranges and the threats to them allows us to be certain that extinction rates are comparable to those of the great past extinctions. For example, for birds, of about 10,000 species worldwide, at least 128 have disappeared in the last 500 years, about 1,200 are currently seriously threatened with extinction (all but three from human activities); there is a real prospect of the loss of 500 bird species within this century.
For less well-known groups, we must use inference. We know there is a rough relationship between the area of a patch of habitat and the number of species it will contain. Since habitat destruction is the leading cause of endangerment and extinction, and we have data on the rate of habitat destruction, we can estimate rates of extinction in some cases. Introduced species, those who migrate to a new area, are the second leading cause of endangerment and extinction. Information on the rate of species introduction and the nature of the impacts of introduced species on native species and ecosystems allows inferences about extinction rates. The evidence all points to a global tragedy with a profound loss of biodiversity.