Advancements in the material design of smart hydrogels have transformed the way therapeutic agents are encapsulated and released in biological environments. On the other hand, the expeditious development of 3D printing technologies has revolutionized the fabrication of hydrogel systems for biomedical applications. By combining these two aspects, 4D printing (i.e., 3D printing of smart hydrogels) has emerged as a new promising platform for the development of novel controlled drug delivery systems that can adapt and mimic natural physio-mechanical changes over time. This allows printed objects to transform from static to dynamic in response to various physiological and chemical interactions, meeting the needs of the healthcare industry. In this review, we provide an overview of innovation in material design for smart hydrogel systems, current technical approaches toward 4D printing, and emerging 4D printed novel structures for drug delivery applications. Finally, we discuss the existing challenges in 4D printing hydrogels for drug delivery and their prospects.