This review covers the new developments in machine learning (ML) that are impacting the multi-disciplinary area of aerospace engineering, including fundamental fluid dynamics (experimental and numerical), aerodynamics, acoustics, combustion and structural health monitoring. We review the state of the art, gathering the advantages and challenges of ML methods across different aerospace disciplines and provide our view on future opportunities. The basic concepts and the most relevant strategies for ML are presented together with the most relevant applications in aerospace engineering, revealing that ML is improving aircraft performance and that these techniques will have a large impact in the near future.