As an important part of soft robots, artificial muscles have received increasing attention. And since artificial muscles are developed by imitating the characteristics of biological muscles, they are naturally suitable for bionic applications. Shape memory alloys (SMAs) have been widely used in the field of artificial muscles due to their high energy density, biocompatibility, corrosion resistance, and self-sensing properties. In this review, the bionic applications of SMA artificial muscles are classified and summarized, and they are divided into two categories: bionic robotics (animal imitation) and biomedical (human imitation) applications. In the part of bionic robots, we summarize the applications of SMA artificial muscles in bionic robots such as flying, jumping, walking, crawling and swimming robots according to the motion characteristics. In the part of biomedical applications, we summarize the applications of SMA artificial muscles in various parts of the human body. In addition, this review also counts the proportion of SMA wires and springs used in applications, and provides a reference for the subsequent selection of SMA wires and springs. Finally, the challenges and opportunities of SMA artificial muscles are summarized and prospected.