Shape memory alloys (SMAs) are a group of metallic alloys capable of sustaining large inelastic strains that can be recovered when subjected to a specific process between two distinct phases. Regarding their unique and outstanding properties, SMAs have drawn considerable attention in various domains and recently became appropriate candidates for origami robots, that require bi-directional rotational motion actuation with limited operational space. However, longitudinal motion-driven actuators are frequently investigated and commonly mentioned, whereas studies in SMA-based rotational motion actuation is still very limited in the literature. This work provides a review of different research efforts related to SMA-based actuators for bi-directional rotational motion (BRM), thus provides a survey and classification of current approaches and design tools that can be applied to origami robots in order to achieve shape-changing. For this purpose, analytical tools for description of actuator behaviour are presented, followed by characterisation and performance prediction. Afterward, the actuators’ design methods, sensing, and controlling strategies are discussed. Finally, open challenges are discussed.