In the debate about the Inference to the Best Explanation, Peter Lipton and Gilbert Harman argue that there are some explanatory virtues or criteria that guide the inferential processes of generation or selection of scientific hypotheses. However, although Lipton lists some of these virtues very briefly in his work, there is no apparent consensus and organization in the philosophy of science literature about what all these criteria are and how they actually operate. The objective of this present article is to (...) offer a taxonomy of these virtues or criteria based on an accurate bibliographic research, proposing an ordering and explanation of each one of them, as well as pointing out a philosophical problem arising from the liptonian approach to IBE. (shrink)