We found that trends in the rate of description of 580,000 marine and terrestrial species, in the taxonomically authoritative World Register of Marine Species and Catalogue of Life databases, were similar until the 1950s. Since then, the relative number of marine to terrestrial species described per year has increased, reflecting the less explored nature of the oceans. From the mid-19th century, the cumulative number of species described has been linear, with the highest number of species described in the decade of 1900, and fewer species described and fewer authors active during the World Wars. There were more authors describing species since the 1960s, indicating greater taxonomic effort. There were fewer species described per author since the 1920s, suggesting it has become more difficult to discover new species. There was no evidence of any change in individual effort by taxonomists. Using a nonhomogeneous renewal process model we predicted that 24-31% to 21-29% more marine and terrestrial species remain to be discovered, respectively. We discuss why we consider that marine species comprise only 16% of all species on Earth although the oceans contain a greater phylogenetic diversity than occurs on land. We predict that there may be 1.8-2.0 million species on Earth, of which about 0.3 million are marine, significantly less than some previous estimates.