Spectacular advances in data acquisition by dense arrays driven by the need for new information, converging interests in academic and private sector applications, and advances in sensor technology are producing fast growing volumes of (high quality) waveform data. On the one hand, this wealth of data gives exciting new opportunities for learning. On the other hand, the risk of data volume growth outpacing compute power and memory poses a formidable challenge for the extraction of increasingly subtle signal from ever expanding data sets. The need to exploit these data calls for revisiting the foundations of the theory of seismic waves, studying their properties and multi-scale interaction with complex, highly heterogeneous media and nonlinear inverse theory, and developing new paradigms for large-scale computing.