The famous Shannon-Nyquist theorem has become a landmark in analog to digital conversion and the development of digital signal processing algorithms. However, in many modern applications, the signal bandwidths have increased tremendously, while the acquisition capabilities have not scaled sufficiently fast. Furthermore, the resulting high rate digital data requires storage, communication and processing at very high rates which is computationally expensive and requires large amounts of power. In this talk we consider a general framework for communication and sensing including sub-Nyquist sampling, quantization and processing in space, time and frequency which allows to dramatically reduce the number of antennas, sampling rates, number of bits and band occupancy in a variety of applications. Our framework relies on exploiting signal structure, quantization and the processing task in both standard processing and in deep learning networks leading to a new framework for model-based deep learning. It also allows for the development of efficient joint radar-communication systems. We consider applications of these ideas to a variety of problems in wireless communications, imaging, efficient massive MIMO systems, automotive radar and ultrasound imaging and show several demos of real-time sub-Nyquist prototypes including a wireless ultrasound probe, sub-Nyquist automotive radar, cognitive radio and radar, dual radar-communication systems, analog precoding, sparse antenna arrays, and a deep Viterbi decoder. We end by discussing more generally how models can be used in deep learning methods with application to a variety of communication settings.