To use artificial intelligence and machine learning models wisely we must understand how they interact with the world, including how they depend causally on data inputs. In this work we develop Causal Dependence Plots (CDPs) to visualize how a model's predicted outcome depends on changes in a given predictor along with consequent causal changes in other predictor variables. Crucially, this differs from standard methods based on independence or holding other predictors constant, such as regression coefficients or Partial Dependence Plots (PDPs). Our explanatory framework generalizes PDPs, including them as a special case, as well as a variety of other interpretive plots that show, for example, the total, direct, and indirect effects of causal mediation. We demonstrate with simulations and real data experiments how CDPs can be combined in a modular way with methods for causal learning or sensitivity analysis. Since people often think causally about input-output dependence, CDPs can be powerful tools in the xAI or interpretable machine learning toolkit and contribute to applications like scientific machine learning and algorithmic fairness.