One of the oldest challenges in ecology is to understand the processes that underpin the composition of communities. Historically, an obvious way in which to describe community compositions has been diversity in terms of the number and abundances of species. However, the failure to reject contradictory models has led to communities now being characterized by trait and phylogenetic diversities. Our objective here is to demonstrate how species, trait and phylogenetic diversity can be combined together from large to local spatial scales to reveal the historical, deterministic and stochastic processes that impact the compositions of local communities. Research in this area has recently been advanced by the development of mathematical measures that incorporate trait dissimilarities and phylogenetic relatedness between species. However, measures of trait diversity have been developed independently of phylogenetic measures and conversely most of the phylogenetic diversity measures have been developed independently of trait diversity measures. This has led to semantic confusions particularly when classical ecological and evolutionary approaches are integrated so closely together. Consequently, we propose a unified semantic framework and demonstrate the importance of the links among species, phylogenetic and trait diversity indices. Furthermore, species, trait and phylogenetic diversity indices differ in the ways they can be used across different spatial scales. The connections between large-scale, regional and local processes allow the consideration of historical factors in addition to local ecological deterministic or stochastic processes. Phylogenetic and trait diversity have been used in large-scale analyses to determine how historical and/or environmental factors affect both the formation of species assemblages and patterns in species richness across latitude or elevation gradients. Both phylogenetic and trait diversity have been used at different spatial scales to identify the relative impacts of ecological deterministic processes such as environmental filtering and limiting similarity from alternative processes such as random speciation and extinction, random dispersal and ecological drift. Measures of phylogenetic diversity combine phenotypic and genetic diversity and have the potential to reveal both the ecological and historical factors that impact local communities. Consequently, we demonstrate that, when used in a comparative way, species, trait and phylogenetic structures have the potential to reveal essential details that might act simultaneously in the assembly of species communities. We highlight potential directions for future research. These might include how variation in trait and phylogenetic diversity alters with spatial distances, the role of trait and phylogenetic diversity in global-scale gradients, the connections between traits and phylogeny, the importance of trait rarity and independent evolutionary history in community assembly, the loss of trait and phylogenetic diversity due to human impacts, and the mathematical developments of biodiversity indices including within-species variations.