Aging ships and offshore structures face harsh environmental and operational conditions in remote areas, leading to age-related damages such as corrosion wastage, fatigue cracking, and mechanical denting. These deteriorations, if left unattended, can escalate into catastrophic failures, causing casualties, property damage, and marine pollution. Hence, ensuring the safety and integrity of aging ships and offshore structures is paramount and achievable through innovative healthcare schemes. One such paradigm, digital healthcare engineering (DHE), initially introduced by the final coauthor, aims at providing lifetime healthcare for engineered structures, infrastructure, and individuals (e.g., seafarers) by harnessing advancements in digitalization and communication technologies. The DHE framework comprises five interconnected modules: on-site health parameter monitoring, data transmission to analytics centers, data analytics, simulation and visualization via digital twins, artificial intelligence-driven diagnosis and remedial planning using machine and deep learning, and predictive health condition analysis for future maintenance. This article surveys recent technological advancements pertinent to each DHE module, with a focus on its application to aging ships and offshore structures. The primary objectives include identifying cost-effective and accurate techniques to establish a DHE system for lifetime healthcare of aging ships and offshore structures—a project currently in progress by the authors.