Pore-scale imaging and modeling has advanced greatly through the integration of Deep Learning into the workflow, from image processing to simulating physical processes. In Digital Core Analysis, a common tool in Earth Sciences, imaging the nano- and micro-scale structure of the pore space of rocks can be enhanced past hardware limitations, while identification of minerals and phases can be automated, with reduced bias and high physical accuracy. Traditional numerical methods for estimating petrophysical parameters and simulating flow and transport can be accelerated or replaced by neural networks. Techniques and common neural network architectures used in Digital Core Analysis are described with a review of recent studies to illustrate the wide range of tasks that benefit from Deep Learning. Focus is placed on the use of Convolutional Neural Networks (CNNs) for segmentation in pore-scale imaging, the use of CNNs and Generative Adversarial Networks (GANs) in image quality enhancement and generation, and the use of Artificial Neural Networks (ANNs) and CNNs for pore-scale physics modeling. Current limitations and challenges are discussed, including advances in network implementations, applications to unconventional resources, dataset acquisition and synthetic training, extrapolative potential, accuracy loss from soft computing, and the computational cost of 3D Deep Learning. Future directions of research are also discussed, focusing on the standardization of datasets and performance metrics, integrated workflow solutions, and further studies in multiphase flow predictions, such as CO2 trapping. The use of Deep Learning at the pore-scale will likely continue becoming increasingly pervasive, as potential exists to improve all aspects of the data-driven workflow, with higher image quality, automated processing, and faster simulations.