There is a high demand for functional smart materials, especially for new material groups in advanced Technologies. These materials are used in the actuator, sensor, control systems, and robotic systems, in addition, they can be hybridized with traditional material to create a particular function. Piezoelectric materials and shape memory alloys are the most important families among these groups. This review includes an overview of shape memory alloys (SMAs) and piezoelectric material actuator systems in terms of robotic applications. The theoretical background of each SMAs and piezoelectric materials is well explained. Different types of each system are interpreted. Using actuator-based SMAs and piezoelectricity in the robotic area is extensively overviewed. Some weaknesses and challenges facing such systems have discussed through recent studies in the literature.