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Evolutionary processes shape the regular trends of evolution and are responsible for the diversity and distribution of contemporary species. They include correlated evolutionary change and trajectories of trait evolution, convergent and parallel evolution, differential rates of evolution, speciation and extinction, the order and direction of change in characters, and the nature of the evolutionary process itself—does change accumulate gradually, episodically, or in punctuational bursts. Phylogenies, in combination with information on species, contain the imprint of these historical evolutionary processes. By applying comparative methods based upon statistical models of evolution to well resolved phylogenies, it is possible to infer the historical evolutionary processes that must have existed in the past, given the patterns of diversity seen in the present. I describe a set of maximum likelihood statistical methods for inferring such processes. The methods estimate parameters of statistical models for inferring correlated evolutionary change in continuously varying characters, for detecting correlated evolution in discrete characters, for estimating rates of evolution, and for investigating the nature of the evolutionary process itself. They also anticipate the wealth of information becoming available to biological scientists from genetic studies that pin down relationships among organisms with unprecedented accuracy.