It is extremely important in many application domains to have transparency in predictive modeling. Domain experts do not tend to prefer "black box" predictive models. They would like to understand how predictions are made, and possibly, prefer models that emulate the way a human expert might make a decision, with a few important variables, and a clear convincing reason to make a particular prediction. I will discuss recent work on interpretable predictive modeling with decision lists and sparse integer linear models. I will describe several approaches, including an algorithm based on discrete optimization, and an algorithm based on Bayesian analysis. I will show examples of interpretable models for stroke prediction in medical patients and prediction of violent crime in young people raised in out-of-home care.