Growing trends towards increased complexity and prolonged useful lives of engineering systems present challenges for system designers in accounting for the impacts of post-design activities (e.g., manufacturing, condition monitoring, remaining life prediction, maintenance, service logistics, end-of-life options, etc.) on system performance (e.g., costs, reliability, customer satisfaction, environmental impacts, etc.). It is very difficult to develop accredited lifecycle system performance models because these activities only occur after the system is built and operated. Thus, system design and post-design decision-making have traditionally been addressed separately, leading to suboptimal performance over the systems lifecycle. With significant advances in computational modeling, simulation, sensing & condition monitoring, and machine learning & artificial intelligence, the capability of predictive modeling has grown prominently over the past decade, leading to demonstrated benefits such as improved system availability and reduced operation and maintenance costs. Predictive modeling can bridge system design and post-design stages and provide an optimal pathway for system designers to effectively account for future system operations at the design stage. In order to achieve optimal performance over the system’s lifecycle, post-design decisions and system operating performance can be incorporated into the initial design with the aid of state-of-the-art predictive modeling approaches. Therefore, optimized design and operation decisions can be explored jointly in an enlarged system design space. This article conducted a literature review for the integrated design and operation of engineering systems with predictive modeling, where not only the predictive modeling approaches but also the strategies of integrating predictive models into the system design processes are categorized. Although predictive modeling has been handled from data-driven, statistical, analytical, and empirical aspects, and recent design problems have started to evaluate the lifecycle performance, there are still challenges in the field that require active investigation and exploration. So, in the end, this article provides a summary of the future directions that encourages research collaborations among the various communities interested in the optimal system lifecycle design.