Developing predictive models that perform reliably across diverse patient populations and heterogeneous environments is a core aim of medical research. However, generalization is only possible if the learned model is robust to statistical differences between data used for training and data seen at the time and place of deployment. Domain generalization methods provide strategies to address data shifts, but each method comes with its own set of assumptions and trade-offs. To apply these methods in healthcare, we must understand how domain shifts arise, what assumptions we prefer to make, and what our design constraints are. This article proposes a causal framework for the design of predictive models to improve generalization. Causality provides a powerful language to characterize and understand diverse domain shifts, regardless of data modality. This allows us to pinpoint why models fail to generalize, leading to more principled strategies to prepare for and adapt to shifts. We recommend general mitigation strategies, discussing trade-offs and highlighting existing work. Our causality-based perspective offers a critical foundation for developing robust, interpretable, and clinically relevant AI solutions in healthcare, paving the way for reliable real-world deployment.