Some people despair that most species will go extinct before they are discovered. However, such worries result from overestimates of how many species may exist, beliefs that the expertise to describe species is decreasing, and alarmist estimates of extinction rates. We argue that the number of species on Earth today is 5 +/- 3 million, of which 1.5 million are named. New databases show that there are more taxonomists describing species than ever before, and their number is increasing faster than the rate of species description. Conservation efforts and species survival in secondary habitats are at least delaying extinctions. Extinction rates are, however, poorly quantified, ranging from 0.01 to 1% (at most 5%) per decade. We propose practical actions to improve taxonomic productivity and associated understanding and conservation of biodiversity.