I will give an overview of a research path in data driven modeling of complex systems over the last 30 or so years – from the early days of shallow neural networks and autoencoders for nonlinear dynamical system identification, to the more recent derivation of data driven “emergent” spaces in which to better learn generative PDE laws. In all illustrations presented, I will try to point out connections between the “traditional” numerical analysis we know and love, and the more modern data-driven tools and techniques we now have – and some mathematical questions they hopefully make possible for us to answer.