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Data streams are ubiquitous in modern business and society. In practice, data streams may evolve over time and cannot be stored indefinitely. Effective and transparent machine learning on data streams is thus often challenging. Hoeffding Trees have emerged as a state-of-the art for online predictive modelling. They are easy to train and provide meaningful convergence guarantees under a stationary process. Yet, at the same time, Hoeffding Trees often require heuristic and costly extensions to adjust to distributional change, which may considerably impair their interpretability. In this work, we revisit Model Trees for machine learning in evolving data streams. Model Trees are able to maintain more flexible and locally robust representations of the active data concept, making them a natural fit for data stream applications. Our novel framework, called Dynamic Model Tree, satisfies desirable consistency and minimality properties. In experiments with synthetic and real-world tabular streaming data sets, we show that the proposed framework can drastically reduce the number of splits required by existing incremental decision trees. At the same time, our framework often outperforms state-of-the-art models in terms of predictive quality -- especially when concept drift is involved. Dynamic Model Trees are thus a powerful online learning framework that contributes to more lightweight and interpretable machine learning in data streams.