During the last few years, smart materials like shape-memory polymers (SMPs) have attracted great attention from manufacturers and researchers due to their ease of formability and functionality. One of the most recent advanced techniques for manufacturing SMPs to create recoverable objects is additive manufacturing (3D printing). The factors that should be considered when printing 3D SMPs include the type of 3D printer being used, the temperature and humidity of the printing environment, and the properties of the shape memory polymer material. Other important parameters include the speed of the printing, the layer thickness, and the size and shape of the object being printed. Another aspect is the infill structure design, which could be regulated to agree with application requirements and achieve feasibility of these polymers. The most famous shapes are honeycomb, gyroid, and triangles. By carefully controlling these parameters, it is possible to achieve high-quality results when 3D printing with SMPs. Infill structure design, such as honeycomb, gyroid, and triangles, can also affect the mechanical characteristics of SMPs, including tensile, bending, and compression strength, as well as shape memory properties such as shape recovery and fixity ratios, and recovery time. Our review comprehensively discusses the influence of printing parameters on the mechanical properties of different SMPs. Future scope for research in this area includes exploring the use of new infill structures, developing techniques for printing multi-material SMPs, and investigating the use of SMPs in novel applications, such as biomedical devices and soft robotics. Overall, by summarizing and quantifying the factors that influence the properties of 3D-printed SMPs, our review provides a valuable resource for researchers and manufacturers looking to improve the production of these materials for various fields. Therefore, summarizing these factors can improve the production of such materials for various fields. The future scope of research in this field includes further exploring the influence of printing parameters on the properties of SMPs, developing new SMP formulations with improved properties, and exploring new applications of 3D-printed SMPs.