Artificial intelligence (AI) has recently become a very popular buzzword, as a consequence of disruptive technical advances and impressive experimental results, notably in the field of image analysis and processing. In medicine, specialties where images are central, like radiology, pathology or oncology, have seized the opportunity and considerable efforts in research and development have been deployed to transfer the potential of AI to clinical applications. With AI becoming a more mainstream tool for typical medical imaging analysis tasks, such as diagnosis, segmentation, or classification, the key for a safe and efficient use of clinical AI applications relies, in part, on informed practitioners. The aim of this review is to present the basic technological pillars of AI, together with the state-of-the-art machine learning methods and their application to medical imaging. In addition, we discuss the new trends and future research directions. This will help the reader to understand how AI methods are now becoming an ubiquitous tool in any medical image analysis workflow and pave the way for the clinical implementation of AI-based solutions.