Mathematical models of the formation and extinction of biological lineages - phylogenetic models - are central to evolutionary biology. Phylogenetic models trace back to the 1925 article by G. Udny Yule in Philosophical Transactions B, “A mathematical theory of evolution, based on the conclusions of Dr. J. C. Willis, F.R.S.” Phylogenetic models have applications in studies of speciation, macroevolution, population genetics, infectious disease epidemiology, the descent of cell lineages, and in investigations of trees as mathematical objects in and of themselves. This theme issue assesses the legacy of Yule’s founding paper 100 years after its publication, describes recent developments in mathematical models of evolutionary trees and networks, and outlines statistical advances in phylogenetic modeling for applications in biology.

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