The paper investigates the constant rate birth-death process, a neutral model for speciation and extinction, conditioned to have \( n \) extant species today. The focus is on the distribution of the reconstructed trees, which are the trees without extinct species. While the tree shape distribution is well-known and identical to the pure birth process, no analytic results for the speciation times were previously available. The authors provide the distribution for the speciation times and calculate their expectations analytically, characterizing the reconstructed trees completely. They show how these results can be used to date phylogenies. The paper also discusses the point process representation of reconstructed trees, the time of origin, and the backward process of reconstructed trees. The methods are implemented in the PhyloTree package and can be used for simulating reconstructed trees and dating phylogenies.The paper investigates the constant rate birth-death process, a neutral model for speciation and extinction, conditioned to have \( n \) extant species today. The focus is on the distribution of the reconstructed trees, which are the trees without extinct species. While the tree shape distribution is well-known and identical to the pure birth process, no analytic results for the speciation times were previously available. The authors provide the distribution for the speciation times and calculate their expectations analytically, characterizing the reconstructed trees completely. They show how these results can be used to date phylogenies. The paper also discusses the point process representation of reconstructed trees, the time of origin, and the backward process of reconstructed trees. The methods are implemented in the PhyloTree package and can be used for simulating reconstructed trees and dating phylogenies.