Detecting distribution shift is crucial for ensuring the safety and integrity of autonomous systems and computational pipelines. Recent advances in deep generative models (DGMs) make them attractive for this use case. However, their application is not straightforward: DGMs fail to detect distribution shift when using naive likelihood thresholds. In this talk, I synthesize the recent literature on using DGMs for out-of-distribution detection. I categorize techniques into two broad classes: model-selection and omnibus methods. I close the talk by arguing that many real-world, safety-critical scenarios require the latter approach.