Soft polymer materials, which are similar to human tissues, have played critical roles in modern interdisciplinary research. Compared with conventional methods, 3D printing allows rapid prototyping and mass customization and is ideal for processing soft polymer materials. However, 3D printing of soft polymer materials is still in the early stages of development and is facing many challenges including limited printable materials, low printing resolution and speed, and poor functionalities. The present review aims to summarize the ideas to address these challenges. It focuses on three points: 1) how to develop printable materials and make unprintable materials printable, 2) how to choose suitable methods and improve printing resolution, and 3) how to directly construct functional structures/systems with 3D printing. After a brief introduction on this topic, the mainstream 3D printing technologies for printing soft polymer materials are reviewed, with an emphasis on improving printing resolution and speed, choosing suitable printing techniques, developing printable materials, and printing multiple materials. Moreover, the state-of-the-art advancements in multimaterial 3D printing of soft polymer materials are summarized. Furthermore, the revolutions brought about by 3D printing of soft polymer materials for applications similar to biology are highlighted. Finally, viewpoints and future perspectives for this emerging field are discussed.