Deep learning (DL) has achieved state-of-the-art performance in many digital pathology analysis tasks. Traditional methods usually require hand-crafted domain-specific features, and DL methods can learn representations without manually designed features. In terms of feature extraction, DL approaches are less labor intensive compared with conventional machine learning methods. In this paper, we comprehensively summarize recent DL-based image analysis studies in histopathology, including different tasks (e.g., classification, semantic segmentation, detection, and instance segmentation) and various applications (e.g., stain normalization, cell/gland/region structure analysis). DL methods can provide consistent and accurate outcomes. DL is a promising tool to assist pathologists in clinical diagnosis.