Generative AI (GenAI), though still in its early stages, is already beginning to transform various industries as a potentially disruptive technology. This paper presents a comprehensive systematic literature review investigating the applications and capabilities of GenAI with a particular focus on its current role in engineering disciplines and the product development process. By synthesizing perspectives from various disciplines that have incorporated GenAI, this review not only examines and showcases the latest progress but also presents challenges of applying GenAI to engineering Design.