Histopathology images; microscopy images of stained tissue biopsies contain fundamental prognostic information that forms the foundation of pathological analysis and diagnostic medicine. However, diagnostics from histopathology images generally rely on a visual cognitive assessment of tissue slides which implies an inherent element of interpretation and hence subjectivity. Access to digitized histopathology images enabled the development of computational systems aiming at reducing manual intervention and automating parts of pathologists' workflow. Specifically, applications of deep learning to histopathology image analysis now offer opportunities for better quantitative modeling of disease appearance and hence possibly improved prediction of disease aggressiveness and patient outcome. However digitized histopathology tissue slides are unique in a variety of ways and come with their own set of computational challenges. In this survey, we summarize the different challenges facing computational systems for digital pathology and provide a review of state-of-the-art works that developed deep learning-based solutions for the predictive modeling of histopathology images from a detection, stain normalization, segmentation, and tissue classification perspective. We then discuss the challenges facing the validation and integration of such deep learning-based computational systems in clinical workflow and reflect on future opportunities for histopathology derived image measurements and better predictive modeling.