While quantum computing has strong potential in data-driven fields, the privacy issue of sensitive or valuable information involved in the quantum algorithm should be considered. Differential privacy (DP), which is a fundamental privacy tool widely used in the classical scenario, has been extended to the quantum domain, i.e., quantum differential privacy (QDP). QDP may become one of the most promising approaches toward privacy-preserving quantum computing since it is not only compatible with classical DP mechanisms but also achieves privacy protection by exploiting unavoidable quantum noise in noisy intermediate-scale quantum (NISQ) devices. This paper provides an overview of the various implementations of QDP and their performance in terms of privacy parameters under the DP setting. Specifically, we propose a taxonomy of QDP techniques, categorizing the literature on whether internal or external randomization is used as a source to achieve QDP and how these implementations are applied to each phase of the quantum algorithm. We also discuss challenges and future directions for QDP. By summarizing recent advancements, we hope to provide a comprehensive, up-to-date review for researchers venturing into this field.