We report ultrahigh bandwidth applications of Kerr microcombs at data rates beyond 10 Terabits/s. Optical neural networks can dramatically accelerate the computing speed to overcome the inherent bandwidth bottleneck of electronics. At the same time, digital signal processing has become central to many fields, from coherent optical telecommunications where it is used to compensate signal impairments, to image processing, important for observational astronomy, medical diagnosis, autonomous driving, big data and particularly artificial intelligence. Digital signal processing had traditionally been performed electronically, but new applications, particularly those involving real time video image processing, are creating unprecedented demand for ultrahigh performance, including bandwidth and reduced energy consumption. We use a new and powerful class of micro-comb called soliton crystals that exhibit robust operation and stable generation as well as a high intrinsic efficiency with a low spacing of 48.9 GHz. We demonstrate a universal optical vector convolutional accelerator operating at 11 Tera-OPS/s (TOPS) on 250,000 pixel images for 10 kernels simultaneously — enough for facial image recognition. We use the same hardware to sequentially form a deep optical CNN with ten output neurons, achieving successful recognition of full 10 digits with 900 pixel handwritten digit images. Finally, we demonstrate a photonic digital signal processor operating at 18 Tb/s and use it to process multiple simultaneous video signals in real-time. The system processes 400,000 video signals concurrently, performing 34 functions simultaneously that are key to object edge detection, edge enhancement and motion blur. As compared with spatial-light devices used for image processing, our system is not only ultra-high speed but highly reconfigurable and programable, able to perform many different functions without any change to the physical hardware. Our approach, based on an integrated Kerr soliton crystal microcomb, opens up new avenues for ultrafast robotic vision and machine learning.