4D printing has a great potential for the manufacturing of soft robotics and medical devices. The alliance of digital light processing (DLP) 3D printing and novel shape-memory photopolymers allows for the fabrication of smart 4D-printed medical devices in high resolution and with tailorable functionalities. However, most of the reported 4D-printed materials are nondegradable, which limits their clinical applications. On the other hand, 4D printing of biodegradable shape-memory elastomers is highly challenging, especially when transition points close to physiological temperature and shape fixation under ambient conditions are required. Here, we report the 4D printing of biodegradable shape-memory elastomers with tailorable transition points covering physiological temperature, by using poly(D,L-lactide-co-trimethylene carbonate) methacrylates at various monomer feed ratios. After the programming step, the high-resolution DLP printed stents preserved their folded shape at room temperature, and showed efficient shape recovery at 37 °C. The materials were cytocompatible and readily degradable under physiological conditions. Furthermore, drug-loaded devices with tuneable release kinetics were realized by DLP-printing with resins containing polymers and levofloxacin or nintedanib. This study offers a new perspective for the development of next-generation 4D-printed medical devices. Digital light 4D printing of biodegradable drug-eluting elastomeric devices with tailorable thermal response at the physiological temperature and tunable drug release. Display omitted •Biodegradable shape-memory elastomers were DLP printed.•The materials displayed elasticity below and above their transition temperatures.•4D printed elastomeric stents showed efficient shape recovery at 37 °C.•4D printed drug-loaded devices showed tuneable release kinetics.