The Earth is a complex dynamic networked system. Machine learning, i.e. derivation of computational models from data, has already made important contributions to predict and understand components of the Earth system, specifically in climate, remote sensing and environmental sciences. For instance, classifications of land cover types, prediction of land-atmosphere and ocean-atmosphere exchange, or detection of extreme events have greatly benefited from these approaches. Such data-driven information has already changed how Earth system models are evaluated and further developed. However, many studies have not yet sufficiently addressed and exploited dynamic aspects of systems, such as memory effects for prediction and effects of spatial context, e.g. for classification and change detection. In particular new developments in deep learning offer great potential to overcome these limitations. Yet, a key challenge and opportunity is to integrate (physical-biological) system modeling approaches with machine learning into hybrid modeling approaches, which combines physical consistency and machine learning versatility. A couple of examples are given with focus on the terrestrial biosphere, where the combination of system-based and machine-learning-based modelling helps our understanding of aspects of the Earth system.