© 2018 American Meteorological Society. Numerical weather, climate, or Earth system models involve the coupling of components. At a broad level, these components can be classified as the resolved fluid dynamics, unresolved fluid dynamical aspects (i.e., those represented by physical parameterizations such as subgrid-scale mixing), and nonfluid dynamical aspects such as radiation and microphysical processes. Typically, each component is developed, at least initially, independently.Once development ismature, the components are coupled to deliver a model of the required complexity. The implementation of the coupling can have a significant impact on the model.As the error associated with each component decreases, the errors introduced by the coupling will eventually dominate. Hence, any improvement in one of the components is unlikely to improve the performance of the overall system. The challenges associated with combining the components to create a coherentmodel are here termed physics-dynamics coupling. The issue goes beyond the coupling between the parameterizations and the resolved fluid dynamics. This paper highlights recent progress and some of the current challenges. It focuses on three objectives: to illustrate the phenomenology of the coupling problemwith references to examples in the literature, to show howthe problem can be analyzed, and to create awareness of the issue across the disciplines and specializations. The topics addressed are different ways of advancing full models in time, approaches to understanding the role of the coupling and evaluation of approaches, coupling ocean and atmosphere models, thermodynamic compatibility between model components, and emerging issues such as those that arise as model resolutions increase and/ormodels use variable resolutions.