Many modern research fields increasingly rely on collecting and analysing massive, often unstructured, and unwieldy datasets. Consequently, there is growing interest in machine learning and artificial intelligence applications that can harness this `data deluge'. This broad nontechnical overview provides a gentle introduction to machine learning with a specific focus on medical and biological applications. We explain the common types of machine learning algorithms and typical tasks that can be solved, illustrating the basics with concrete examples from healthcare. Lastly, we provide an outlook on open challenges, limitations, and potential impacts of machine-learning-powered medicine.