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Medical ultrasound imaging relies heavily on high-quality signal processing to provide reliable and interpretable image reconstructions. Conventionally, reconstruction algorithms where derived from physical principles. These algorithms rely on assumptions and approximations of the underlying measurement model, limiting image quality in settings were these assumptions break down. Conversely, more sophisticated solutions based on statistical modelling, careful parameter tuning, or through increased model complexity, can be sensitive to different environments. Recently, deep learning based methods, which are optimized in a data-driven fashion, have gained popularity. These model-agnostic techniques often rely on generic model structures, and require vast training data to converge to a robust solution. A relatively new paradigm combines the power of the two: leveraging data-driven deep learning, as well as exploiting domain knowledge. These model-based solutions yield high robustness, and require less parameters and training data than conventional neural networks. In this work we provide an overview of these techniques from recent literature, and discuss a wide variety of ultrasound applications. We aim to inspire the reader to further research in this area, and to address the opportunities within the field of ultrasound signal processing. We conclude with a future perspective on model-based deep learning techniques for medical ultrasound.