The time domain is the emerging forefront of astronomical research with new facilities and instruments providing unprecedented amounts of data on the temporal behavior of astrophysical populations. Dealing with the size and complexity of this requires new techniques and methodologies. Quasars are an ideal work set for developing and applying these: they vary in a detectable but not easily quantifiable manner whose physical origins are poorly understood. In this paper, we will review how quasars are identified by their variability and how these techniques can be improved, what physical insights into their variability can be gained from studying extreme examples of variability, and what approaches can be taken to increase the number of quasars known. These will demonstrate how astroinformatics is essential to discovering and understanding this important population.