A principal function of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES) is to “perform regular and timely assessments of knowledge on biodiversity.” In December 2013, its second plenary session approved a program to begin a global assessment in 2015. The Convention on Biological Diversity (CBD) and five other biodiversity-related conventions have adopted IPBES as their science-policy interface, so these assessments will be important in evaluating progress toward the CBD’s Aichi Targets of the Strategic Plan for Biodiversity 2011–2020. As a contribution toward such assessment, we review the biodiversity of eukaryote species and their extinction rates, distributions, and protection. We document what we know, how it likely differs from what we do not, and how these differences affect biodiversity statistics. Interestingly, several targets explicitly mention “known species”—a strong, if implicit, statement of incomplete knowledge. We start by asking how many species are known and how many remain undescribed. We then consider by how much human actions inflate extinction rates. Much depends on where species are, because different biomes contain different numbers of species of different susceptibilities. Biomes also suffer different levels of damage and have unequal levels of protection. How extinction rates will change depends on how and where threats expand and whether greater protection counters them.