Compound decision theory is a classical area of statistics that is now experiencing a resurgence of interest. Current work is dominated by empirical Bayes approaches with desirable theoretical and empirical properties. However, empirical Bayes methods may not be flexible enough to accommodate more complicated problems. This talk will 1) describe a new regression modeling perspective on compound decision problems, 2) present new flexible estimation procedures motivated by this perspective, and 3) develop new methods for several problems in genomics that are particularly amenable to compound decision-based approaches.