The domain of aeronautical engineering and aero-engine engineering has witnessed considerable interest in the application of machine learning (ML) and deep learning (DL) techniques, revolutionizing various aspects of the field. This review provides a comprehensive review of the application of ML and DL in aerospace engineering and aero-engine engineering, focusing on aircraft aerodynamics, CFD, aircraft design and aeroacoustics and for aero-engine engineering focusing on health state evaluation, component optimization, blade defect detection and combustion. The review highlights the advantages and challenges of ML methods, presenting key concepts and strategies for ML. Furthermore, in terms of technical applications, DL has the potential to be on par with ML, despite being a branch of ML. The review further emphasizes the pressing requirement for a comprehensive examination of DL techniques concerning data-driven challenges within the realms of aerospace engineering and aero-engine engineering. It introduces representative DL methods and presents their mathematical definitions and illustrative applications.