Machine learning and AI algorithms are transforming a diverse number of fields in science and engineering. This is largely due to their success in model discovery which turns data into reduced order models and neural network representations that are not just predictive, but provide insight into the nature of the underlying dynamical system that generated the data. We introduce a number of data-driven strategies, including targeted uses of deep learning, for discovering nonlinear multiscale dynamical systems, compact representations, and their embeddings from data. Importantly, data-driven architectures must jointly discover coordinates and parsimonious models in order to produce maximally generalizable and interpretable models of physics-based systems and processes.