Four-dimensional (4D) printing technology, as a next-generation additive manufacturing method, enables printed objects to further change their shapes, functionalities, or properties upon exposure to external stimuli. The 4D printing of programmable and deformable materials such as thermo-responsive shape-memory polymers (trSMPs), which possess the ability to change shape by exposure to heat, has attracted particular interest in recent years. Three-dimensional objects based on SMPs have been proposed for various potential applications in different fields, including soft robotics, smart actuators, biomedical and electronics. To enable the manufacturing of complex multifunctional 3D objects, SMPs are often coupled with other functional polymers or fillers during or before the 3D printing process. This review highlights the 4D printing of state-of-the-art multi-component SMP formulations. Commonly used 4D printing technologies such as material extrusion techniques including fused filament fabrication (FFF) and direct ink writing (DIW), as well as vat photopolymerization techniques such as stereolithography (SLA), digital light processing (DLP), and multi-photon polymerization (MPP), are discussed. Different multicomponent SMP systems, their actuation methods, and potential applications of the 3D printed objects are reviewed. Finally, current challenges and prospects for 4D printing technology are summarized.