Understanding how and why rates of evolutionary diversification vary is a central issue in evolutionary biology, ecology and biogeography. The concept of adaptive radiation has attracted much interest, but is metaphorical and verbal in nature, making it difficult to quantitatively compare different evolutionary lineages or geographic regions. In addition, the causes of evolutionary stasis are relatively neglected. Here we review the central concepts in the evolutionary diversification literature and bring these together by proposing a general framework for studying rates of diversification and quantifying their underlying dynamics, which can be applied across clades and regions and across spatial and temporal scales. Our framework describes the diversification rate (d) as a function of the abiotic environment (a), the biotic environment (b) and clade-specific phenotypes or traits (c); thus d ~ a, b, c. We refer to the four components (a–d) and their interactions collectively as the ‘Evolutionary Arena’. We outline analytical approaches to this conceptual model that may open up new avenues for research, and present a case study on conifers, for which we parameterise the general model. We also discuss three conceptual examples based on existing literature: the Lupinusradiation in the Andes in the context of emerging ecological opportunity and fluctuating connectivity due to climatic oscillations; oceanic island radiations in the context of archipelago isolation and island formation and erosion; and biotically driven radiations of the Mediterranean orchid genus Ophrys. The results of the conifer case study are consistent with the long-standing scenario that large niches, lack of competition, and high rates of niche evolution differentially promote diversification. The conceptual examples illustrate how using the synthetic Evolutionary Arena framework results in highlighting gaps in current knowledge, and thus help to identify and structure future directions for research on evolutionary radiations. In this way, the Evolutionary Arena framework promotes a more general understanding of variation in evolutionary rates by making quantitative results comparable between case studies, thereby allowing new syntheses of evolutionary and ecological processes to emerge.