With the advantages of simple structure, low power consumption, no electromagnetic interference, and fast response, piezoelectric pumps (PPs) have been widely used in the fields of chip cooling, biomedical applications, chemical applications, and fuel supply applications. In recent decades, scholars have proposed various PPs, and this article reviews the recent research results. In this review, according to the “valve” structure, PPs are divided into valve-less piezoelectric pumps (VLPPs), valve-based piezoelectric pumps (VBPPs), and piezoelectric pumps with valve and valve-less state transitions (PPVVSTs). Firstly, the design methods of typical structures were discussed, and comparisons were made in terms of driving frequency, driving voltage, output pressure, flow rate, structure materials, and pump size. The advantages and disadvantages of VLPPs, VBPPs, and PPVVSTs were analyzed. Then, we compared the driving parameters, output performance, structure materials, and pump size of single-chamber piezoelectric pumps (SCPs) and multi-chamber piezoelectric pumps (MCPs) and analyzed the advantages and disadvantages of SCPs and MCPs. Optimization methods proposed in recent years have been summarized to address the issues of the cavitation phenomenon, the liquid back-flow problem, and low output performance in PPs. Subsequently, the application research of PPs and the distribution of academic achievements were discussed. Finally, this review was summarized, and future research hot spots for PPs were proposed. The main contribution of this review is to provide piezoelectric pump (PP) researchers with a certain understanding of the structural design, optimization methods, practical applications, and research distribution of PPs, which can provide theoretical guidance for future research.