Explaining artificial intelligence or machine learning models is increasingly important. To use such data-driven systems 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 one variable---a predicted outcome---depends on changes in another variable---a predictor---along with consequent causal changes in other predictor variables. Crucially, this may differ from standard methods based on holding other predictors constant or assuming they are independent, such as regression coefficients or Partial Dependence Plots (PDPs). CDPs use an auxiliary causal model to produce explanations because causal conclusions require causal assumptions. Our explanatory framework generalizes PDPs, including them as a special case, and enables a variety of other custom interpretive plots to 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.