Natural polymers are organic compounds produced by living organisms. In nature, they exist in three main forms, including proteins, polysaccharides, and nucleic acids. In recent years, with the continuous research on drug and gene delivery systems, scholars have found that natural polymers have promising applications in drug and gene delivery systems due to their excellent properties such as biocompatibility, biodegradability, low immunogenicity, and easy modification. However, since the structure, physicochemical properties, pharmacological properties and biological characteristics of biopolymer molecules have not yet been entirely understood, further studies are required before large-scale clinical application. This review focuses on recent advances in the representative natural polymers such as proteins (albumin, collagen, elastin), polysaccharides (chitosan, alginate, cellulose) and nucleic acids. We introduce the characteristics of various types of natural polymers, and further outline the characterization methods and delivery forms of these natural polymers. Finally, we discuss possible challenges for natural polymers in subsequent experimental studies and clinical applications. It provides an important strategy for the clinical application of natural polymers in drug and gene delivery systems.