The field of phylodynamics focuses on the problem of reconstructing population size dynamics over time using current genetic samples taken from the population of interest. This technique has been extensively used in many areas of biology but is particularly useful for studying the spread of quickly evolving infectious diseases agents, e.g. influenza virus. Phylodynamic inference uses a coalescent model that defines a probability density for the genealogy of randomly sampled individuals from the population. When we assume that such a genealogy is known, the coalescent model, equipped with a Gaussian process prior on population size trajectory, allows for nonparametric Bayesian estimation of population size dynamics. Although this approach is quite powerful, large datasets collected during infectious disease surveillance challenge the state-of-the-art of Bayesian phylodynamics and demand inferential methods with relatively low computational cost.