By transferring the knowledge of the source domain to the target domain with similar tasks, domain adaptation aims to assist the latter to learn better. When the data label set of the target domain is a subset of the source domain labels, the domain adaptation of this type of scenario is called partial domain adaptation (PDA). Compared with general domain adaptation, although PDA is more general, it is more challenging with few related studies, especially with the lack of systematic reviews. To fill this gap, this study conducts a comprehensive review, analysis and summary of existing PDA methods, and provides an overview and reference of subject research for the relevant community. Firstly, an overview of the PDA background, concepts, and application fields is summarized. Secondly, according to the modeling characteristics, existing PDA methods are divided into two categories: promoting positive transfer and alleviating negative transfer, and this study reviews and analyzes them respectively. Then, the commonly used experimental benchmark datasets are categorized and summarized. Finally, the problems in existing PDA studies are analyzed to point out possible future development directions.