The coalescent is a central modeling framework in modern population genetics and evolutionary biology. Coalescent models provide robust approximations to the distribution of sampled genealogies under a variety of population dynamics and allow us to express genealogical tree priors in terms of population parameters of interest. Point process constructions of these models have proven to be an exceptionally fruitful mathematical approach. In this talk, I will present three new instances in which point processes constructions facilitate the derivation of novel coalescent priors and simulation. In particular, we derive the coalescent distribution under epidemiological disease dynamics with latent periods, under linear birth-death dynamics and when the TMRCA is bounded (bounded coalescent).