With the explosive growth of Big Data and the emergence of general purpose computing with graphics processing units, Deep Learning has seen rapid adoption in many industries including healthcare, finance, entertainment, architecture, engineering, social media, speech recognition and translation, retail, advertising, high-performance computing, robotics, and transportation. Deep Learning is a rapidly growing class of Artificial Intelligence which has shown tremendous promise for solving heretofore intractable problems. To date, the adoption of Deep Learning techniques has been somewhat limited in the Modeling, Simulation, and Training (MS&T) community. However, there are many possibilities for leveraging the work from other industries for the benefit of MS&T. Much of the active research in Deep Learning has direct relation to problems faced by the MS&T community, including image classification and segmentation, texture synthesis, physically-based material generation, ray tracing, style transfer, natural language processing, gaze tracking, character animation, and human behavior modeling. In this paper, we will first provide an overview of Deep Learning concepts and how it fits into the broader contexts of Artificial Intelligence and Machine Learning. We then present the state-of-the-art in Deep Learning, including convolutional neural networks, generative adversarial networks, and phase-functioned neural networks. Finally, we discuss some of the ways that advancements in Deep Learning can be applied to meet current and future requirements in MS&T.