Although the Earth is biodiverse, the extent of this diversity is largely unknown. Various approaches are available to estimate species numbers, ranging from expert opinions to extrapolation from macroecological patterns to estimates from known taxonomic patterns. Taxonomic specialists suggest an order of magnitude estimation. Scaling from local/regional richness or body size distributions to global diversity provides more accurate estimates and demonstrates the importance of these traits. The most empirically reliable method utilizes species accumulation and taxonomic effort. In chapter 2, a more widely applicable model that refines previous methods was developed by assuming a Poisson distribution for species described in time intervals, then using maximum likelihood to estimate the parameters for an unknown intensity function.Estimates of species numbers provide information only on the scope of unknown diversity. Biological and ecological traits associated with the likelihood of species discovery suggest a guide for taxonomic investigations. In chapter 3, a survival analysis indicated correlations between several traits across all mammals and within the most populous mammalian orders. Like previous studies, geographic range size and adult body mass are the most important traits in species discovery across all mammals. Within some orders (i.e., Chiroptera and Diprotodontia) human population density is also an important predictor. Taxonomic order and biogeographic realm are the most important in the earliest time period of species discovery and geographic range size increases in importance over time. Overall, undiscovered species are small, have small ranges, are tropical dwellers far from human populations, and have small litters.To date, studies of discovery correlates have been across higher taxa (order and above). Chapter 4 presents analyses performed at a lower taxonomic level, a single family of rodents (Muridae), to assess if patterns of species numbers and discovery correlates are mirror those in higher taxa. Like all mammals, 5% of murids remain unknown and geographic range size is the most important discovery correlate. In contrast, genus is second and body size is last in importance for murids. These global studies of discovery offer similar results at varying taxonomic levels, suggesting that the methods employed here may provide broader insights about unknown species.