Shape-memory materials are smart materials that can remember an original shape and return to their unique state from a deformed secondary shape in the presence of an appropriate stimulus. This property allows these materials to be used as shape-memory artificial muscles, which form a subclass of artificial muscles. The shape-memory artificial muscles are fabricated from shape-memory polymers (SMPs) by twist insertion, shape fixation via T_m or T_g, or by liquid crystal elastomers (LCEs). The prepared SMP artificial muscles can be used in a wide range of applications, from biomimetic and soft robotics to actuators, because they can be operated without sophisticated linkage design and can achieve complex final shapes. Recently, significant achievements have been made in fabrication, modelling, and manipulation of SMP-based artificial muscles. This paper presents a review of the recent progress in shape-memory polymer-based artificial muscles. Here we focus on the mechanisms of SMPs, applications of SMPs as artificial muscles, and the challenges they face concerning actuation. While shape-memory behavior has been demonstrated in several stimulated environments, our focus is on thermal-, photo-, and electrical-actuated SMP artificial muscles.