This review explores the intersection of Artificial Intelligence (AI) and Generative Design (GD) in engineering within the mechanical, industrial, civil, and architectural domains. Driven by advances in AI and computational resources, this intersection has grown rapidly, yielding over 14,000 publications since 2016. To map the research landscape, this review employed semantic search and Natural Language Processing, parsing 14,355 publications to ultimately select the 88 most relevant studies through clustering and topic modelling. These studies were categorised according to AI and GD techniques, application domains, benefits, and limitations, providing insights into research trends and practical implications. The results reveal a significant growth in the integration of advanced generative AI methods, notably Generative Adversarial Networks for direct design generation, alongside the continued use of genetic algorithms and surrogate models (e.g., Convolutional Neural Networks and Multilayer Perceptrons) to manage computational complexity. Structural and aerodynamic applications were the most common, with benefits including improvements in computational efficiency and design diversity. However, barriers remain, including data generation costs, model accuracy, and interpretability. Research opportunities include the development of generalisable foundation surrogate models, the integration of emerging generative methods such as diffusion models and large language models, and the explicit consideration of manufacturability constraints within generative processes.