The precision-based revolution in medicine continues to demand stratification of patients into smaller and more personalized subgroups. While genomic technologies have largely led this movement, diagnostic results can take days to weeks to generate. Management at, or closer to, the point of care still heavily relies on the subjective qualitative interpretation of clinical and diagnostic imaging findings. New and emerging technological advances in artificial intelligence (AI) now appear poised to help bring objectivity and precision to these traditionally qualitative analytic tools. In particular, one specific form of AI, known as deep learning, is achieving expert-level disease classifications in many areas of diagnostic medicine dependent on visual and image-based findings. Here, we briefly review concepts of deep learning, and more specifically recent developments in convolutional neural networks (CNNs), to highlight their transformative potential in personalized medicine and, in particular, diagnostic histopathology. Understanding the opportunities and challenges of these quantitative machine-based decision support tools is critical to their widespread introduction into routine diagnostics.