In the last few decades, there has been a remarkable discovery of new species of plants, invertebrates and vertebrates, in what have been called the new age of discovery. However, owing to anthropogenic impacts such as habitat conversion, many of the still unknown species may go extinct before being scientifically documented (i.e. 'crypto-extinctions'). Here, by applying a mathematical model of species descriptions which accounts for taxonomic effort, we show that even after 250 years of taxonomic classification, about 3050 amphibians and at least 160 land mammal species remain to be discovered and described. These values represent, respectively, 33 and 3 per cent of the current species total for amphibians and land mammals. We found that tropical moist forests of the Neotropics, Afrotropics and Indomalaya probably harbour the greatest numbers of undescribed species. Tropical forests with minimal anthropogenic disturbance are predicted to have larger proportions of undescribed species. However, the protected area coverage is low in many of these key biomes. Moreover, undescribed species are likely to be at a greater risk of extinction compared with known species because of small geographical ranges among other factors. By highlighting the key areas of undescribed species diversity, our study provides a starting template to rapidly document these species and protect them through better habitat management.