Approaches to macroevolution require integration of its two fundamental components, within a hierarchical framework. Following a companion paper on the origin of variation, I here discuss sorting within an evolutionary hierarchy. Species sorting—sometimes termed species selection in the broad sense, meaning differential origination and extinction owing to intrinsic biological properties—can be split into strict-sense species selection, in which rate differentials are governed by emergent, species-level traits such as geographic range size, and effect macroevolution, in which rates are governed by organism-level traits such as body size; both processes can create hitchhiking effects, indirectly causing the proliferation or decline of other traits. Several methods can operationalize the concept of emergence, so that rigorous separation of these processes is increasingly feasible. A macroevolutionary tradeoff, underlain by the intrinsic traits that influence evolutionary dynamics, causes speciation and extinction rates to covary in many clades, resulting in evolutionary volatility of some clades and more subdued behavior of others; the few clades that break the tradeoff can achieve especially prolific diversification. In addition to intrinsic biological traits at multiple levels, extrinsic events can drive the waxing and waning of clades, and the interaction of traits and events are difficult but important to disentangle. Evolutionary trends can arise in many ways, and at any hierarchical level; descriptive models can be fitted to clade trajectories in phenotypic or functional spaces, but they may not be diagnostic regarding processes, and close attention must be paid to both leading and trailing edges of apparent trends. Biotic interactions can have negative or positive effects on taxonomic diversity within a clade, but cannot be readily extrapolated from the nature of such interactions at the organismic level. The relationships among macroevolutionary currencies through time (taxonomic richness, morphologic disparity, functional variety) are crucial for understanding the nature of evolutionary diversification. A novel approach to diversity-disparity analysis shows that taxonomic diversifications can lag behind, occur in concert with, or precede, increases in disparity. Some overarching issues relating to both the origin and sorting of clades and phenotypes include the macroevolutionary role of mass extinctions, the potential differences between plant and animal macroevolution, whether macroevolutionary processes have changed through geologic time, and the growing human impact on present-day macroevolution. Many challenges remain, but progress is being made on two of the key ones: (a) the integration of variation-generating mechanisms and the multilevel sorting processes that act on that variation, and (b) the integration of paleontological and neontological approaches to historical biology.