We might hope that when faced with unexpected inputs, well-designed software systems would fire off warnings. However, ML systems, which depend strongly on properties of their inputs (e.g. the i.i.d. assumption), tend to fail silently. Faced with distribution shift, we wish (i) to detect and (ii) to quantify the shift, and (iii) to correct our classifiers on the fly—when possible. This talk will describe a line of recent work on tackling distribution shift. First, I will focus on recent work on label shift, a more classic problem, where strong assumptions enable principled methods. Then I will discuss how recent tools from generative adversarial networks have been appropriated (and misappropriated) to tackle dataset shift—characterizing and (partially) repairing a foundational flaw in the method.