There have been five Mass Extinction events in the history of Earth's biodiversity, all caused by dramatic but natural phenomena. It has been claimed that the Sixth Mass Extinction may be underway, this time caused entirely by humans. Although considerable evidence indicates that there is a biodiversity crisis of increasing extinctions and plummeting abundances, some do not accept that this amounts to a Sixth Mass Extinction. Often, they use the IUCN Red List to support their stance, arguing that the rate of species loss does not differ from the background rate. However, the Red List is heavily biased: almost all birds and mammals but only a minute fraction of invertebrates have been evaluated against conservation criteria. Incorporating estimates of the true number of invertebrate extinctions leads to the conclusion that the rate vastly exceeds the background rate and that we may indeed be witnessing the start of the Sixth Mass Extinction. As an example, we focus on molluscs, the second largest phylum in numbers of known species, and, extrapolating boldly, estimate that, since around AD 1500, possibly as many as 7.5-13% (150,000-260,000) of all ~2 million known species have already gone extinct, orders of magnitude greater than the 882 (0.04%) on the Red List. We review differences in extinction rates according to realms: marine species face significant threats but, although previous mass extinctions were largely defined by marine invertebrates, there is no evidence that the marine biota has reached the same crisis as the non-marine biota. Island species have suffered far greater rates than continental ones. Plants face similar conservation biases as do invertebrates, although there are hints they may have suffered lower extinction rates. There are also those who do not deny an extinction crisis but accept it as a new trajectory of evolution, because humans are part of the natural world; some even embrace it, with a desire to manipulate it for human benefit. We take issue with these stances. Humans are the only species able to manipulate the Earth on a grand scale, and they have allowed the current crisis to happen. Despite multiple conservation initiatives at various levels, most are not species oriented (certain charismatic vertebrates excepted) and specific actions to protect every living species individually are simply unfeasible because of the tyranny of numbers. As systematic biologists, we encourage the nurturing of the innate human appreciation of biodiversity, but we reaffirm the message that the biodiversity that makes our world so fascinating, beautiful and functional is vanishing unnoticed at an unprecedented rate. In the face of a mounting crisis, scientists must adopt the practices of preventive archaeology, and collect and document as many species as possible before they disappear. All this depends on reviving the venerable study of natural history and taxonomy. Denying the crisis, simply accepting it and doing nothing, or even embracing it for the ostensible benefit of humanity, are not appropriate options and pave the way for the Earth to continue on its sad trajectory towards a Sixth Mass Extinction.