Predictions of the Earth system, such as weather forecasts and climate projections, require models informed by observations at many levels. Some methods for integrating models and observations are very systematic and comprehensive (e.g., data assimilation), and some are single purpose and customized (e.g., for model validation). We review current methods and best practices for integrating models and observations. We highlight how future developments can enable advanced heterogeneous observation networks and models to improve predictions of the Earth system (including atmosphere, land surface, oceans, cryosphere, and chemistry) across scales from weather to climate. As the community pushes to develop the next generation of models and data systems, there is a need to take a more holistic, integrated, and coordinated approach to models, observations, and their uncertainties to maximize the benefit for Earth system prediction and impacts on society.