Forthcoming massive astronomical data sets are poised to revolutionize the way we do astronomy. However, such complex data sets present both methodological and computational challenges. In this talk I will discuss some of the methods that I have developed for tackling these challenges, as applied to two astronomical problems. First, I will discuss my work on investigating the growth and evolution of the supermassive black hole population as inferred from the quasar black hole mass and Eddington ratio functions from the SDSS. I will discuss a novel method that I have developed for correcting for the uncertainty and incompleteness in these quantities, and highlight the different scientific conclusions regarding the black hole population obtained from my method compared to traditional methods. Second, I will discuss robust and computationally fast methods for characterizing the variability of lightcurves. These methods fully account for irregular sampling and measurement errors and provide a basis for effective and efficient selection of different types of variables. I will discuss my use of these methods for investigating accretion physics via quasar variability. I will conclude by discussing future work on extending and using these methods to study astronomical populations in the era of DES, Pan-STARRS, and LSST.