Piezoelectric stick-slip actuators (PSSAs) are famous for ultimate working condition adaptability, simple structure, and positioning accuracy. To meet the demand of industrial application, lots of PSSAs designed with flexure hinge mechanisms (FHMs-PSSAs) have been developed to realize the requirements of translational motion, rotational motion, multi-degree-of-freedom (multi-DOF) motion. The output performance of the FHMs-PSSAs has been greatly improved, including load capacity, speed, and accuracy; moreover, some approaches to solve the problem of the backward motion are provided as well. In this work, the working principle of FHMs-PSSAs is introduced, and the excitation signals applicable to FHMs-PSSAs are summarized. Based on the current research and development status, the progress of structure design of FHMs-PSSAs is introduced in accordance with translatory FHMs-PSSAs, rotary FHMs-PSSAs, and multi-DOF FHMs-PSSAs. Additionally, the developed analysis methods and design schemes to improve the performance are introduced, including theoretical analysis methods, consistency scheme of forward and reverse performance, suppression scheme of the backward motion, and improvement scheme of positioning accuracy. The significance of this work can be regarded as a further supplement to the previous review articles on the PSSAs, which will provide a reference and guidance for the future development of FHMs-PSSAs.