The concept of biological diversity, or biodiversity, is at the core of evolutionary and ecological studies. Many indices of biodiversity have been developed in the last four decades, with species being one of the central units of these indices. However, evolutionary and ecological studies need a precise description of species' characteristics to best quantify inter‐species diversity, as species are not equivalent and exchangeable. One of the first concepts characterizing species in biodiversity studies was abundance‐based rarity. Abundance‐based rarity was then complemented by trait‐ and phylo‐based rarity, called species' trait‐based and phylogenetic originalities, respectively. Originality, which is a property of an individual species, represents a species' contribution to the overall diversity of a reference set of species. Originality can also be defined as the rarity of a species' characteristics such as the state of a functional trait, which is often assumed to be represented by the position of the species on a phylogenetic tree. We review and compare various approaches for measuring originality, rarity and diversity and demonstrate that (i) even if attempts to bridge these concepts do exist, only a few ecological and evolutionary studies have tried to combine them all in the past two decades; (ii) phylo‐ and trait‐based diversity indices can be written as a function of species rarity and originality measures in several ways; and (iii) there is a need for the joint use of these three types of indices to understand community assembly processes and species' roles in ecosystem functioning in order to protect biodiversity efficiently.