Deep neural networks provide unprecedented performance gains in many real-world problems in signal and image processing. Despite these gains, the future development and practical deployment of deep networks are hindered by their black-box nature, i.e., a lack of interpretability and the need for very large training sets. On the other hand, signal processing and communications have traditionally relied on classical statistical modeling techniques that utilize mathematical formulations representing the underlying physics, prior information and additional domain knowledge. Simple classical models are useful but sensitive to inaccuracies and may lead to poor performance when real systems display complex or dynamic behavior. Here we introduce various approaches to model based learning which merge parametric models with optimization tools and classical algorithms leading to efficient, interpretable networks from reasonably sized training sets. We then show how model based signal processing can impact federated learning both in terms of communication efficiency and in terms of convergence properties. We will consider examples to image deblurring, super resolution in ultrasound and microscopy, efficient communication systems, and efficient diagnosis of COVID19 using X-ray and ultrasound.