Breast cancer is the most common malignant disease in women worldwide. In recent decades, earlier diagnosis and better adjuvant therapy have substantially improved patient outcome. Diagnosis by histopathology has proven to be instrumental to guide breast cancer treatment, but new challenges have emerged as our increasing understanding of cancer over the years has revealed its complex nature. As patient demand for personalized breast cancer therapy grows, we face an urgent need for more precise biomarker assessment and more accurate histopathologic breast cancer diagnosis to make better therapy decisions. The digitization of pathology data has opened the door to faster, more reproducible, and more precise diagnoses through computerized image analysis. Software to assist diagnostic breast pathology through image processing techniques have been around for years. But recent breakthroughs in artificial intelligence (AI) promise to fundamentally change the way we detect and treat breast cancer in the near future. Machine learning, a subfield of AI that applies statistical methods to learn from data, has seen an explosion of interest in recent years because of its ability to recognize patterns in data with less need for human instruction. One technique in particular, known as deep learning, has produced groundbreaking results in many important problems including image classification and speech recognition. In this review, we will cover the use of AI and deep learning in diagnostic breast pathology, and other recent developments in digital image analysis.