Stellar masses, and the ages inferred from them, are a fundamental element in our studies of stellar populations in the Milky Way, and so have wide ranging impacts on our constraints on models of galaxy formation and evolution. The recent advent of long duration, short cadence photometry for large samples of stars has brought asteroseismology, the study of stellar oscillations, to the fore as one of the most precise techniques for ascertaining the masses of stars. With the training data provided by asteroseismic samples, in combination with extensive spectroscopic survey data for the same stars, we can now train models that can predict the masses and ages of red giants over a large range of radii in the Milky Way. In this talk I will present new statistical and machine learning methods which have been developed for estimating the ages of Milky Way stellar populations and recent constraints on the Milky Way formation and evolution that have been made using them. At the same time, I will show how improvements in the asteroseismic training data are allowing such models to be further improved, as well as outlining the future directions that will only improve these methods. Finally, I will discuss how machine learning applications to the asteroseismic data are about to also revolutionise this field, as surveys such as TESS provide this data on an all-sky basis.