PolieDRO is a novel analytics framework with applications to both predictive and prescriptive realms. It harnesses the power and flexibility of Data-Driven Distributionally Robust Optimization (DRO) to circumvent the need for regularization hyperparameters, while extracting structure from the underlying data. In the field of predictive modeling, recent literature shows that traditional machine learning methods such as SVM and (square-root) LASSO can be written as Wasserstein-based DRO problems. Inspired by those results we propose a hyperparameter-free ambiguity set that explores the polyhedral structure of data-driven convex hulls, generating computationally tractable regression and classification methods for any convex loss function. Numerical results based on 100 real-world databases and an extensive experiment with synthetically generated data show that our methods consistently outperform their traditional counterparts. In the prescriptive realm, we develop a portfolio optimization model that employs the DRO approach simultaneously at the risk and return levels. Applying this model to real financial data spanning several decades, we achieve consistent superior performance compared to a benchmark.