Ecologists widely agree that species diversity consists of two components, richness (the number of species) and evenness (a measure of the equitability of the proportional abundances of those species). However, no consensus on an exact definition of evenness (or equitability) has emerged. Instead, numerous equitability indices have been used in the ecological literature, as different researchers have preferred indices with different mathematical properties. In this paper, I show that the phrase ‘species diversity consists of two independent components, richness and evenness’ logically leads to one particular definition of evenness (Evenness = Diversity/Richness). To facilitate accurate communication, I propose that the term ‘evenness’ be used only to refer to this phenomenon, and that other terms be used for the equitability indices that measure other things. Here I provide a review of popular equitability indices, explain what each measures in practice, and show how they relate to each other and to evenness itself. I also explore how the partitioning of diversity into richness and evenness components is related to the partitioning of diversity into alpha and beta components. Dissecting the indices makes it easier to see the conceptual differences among them. Such understanding is necessary to ensure that an appropriate index is chosen for the questions at hand, as well as to interpret the index values correctly and to assess when index values can and when they cannot be considered comparable.