Alloy modelling has a history of machine-learning-like approaches, preceding the tide of data-science-inspired work. The dawn of computational databases has made the integration of analysis, prediction and discovery the key theme in accelerated alloy research. Advances in machine-learning methods and enhanced data generation have created a fertile ground for computational materials science. Pairing machine learning and alloys has proven to be particularly instrumental in pushing progress in a wide variety of materials, including metallic glasses, high-entropy alloys, shape-memory alloys, magnets, superalloys, catalysts and structural materials. This Review examines the present state of machine-learning-driven alloy research, discusses the approaches and applications in the field and summarizes theoretical predictions and experimental validations. We foresee that the partnership between machine learning and alloys will lead to the design of new and improved systems.