The potato has recently attracted more attention as a promising protein source. Potato proteins are commonly extracted from potato fruit juice, a byproduct of starch production. Potato proteins are characterized by superior techno-functional properties, such as water solubility, gel-forming, emulsifying, and foaming properties. However, commercially isolated potato proteins are often denatured, leading to a loss of these functionalities. Extensive research has explored the influence of different conditions and techniques on the emulsifying capacity and stability of potato proteins. However, there has been no comprehensive review of this topic yet. This paper aims to provide an in-depth overview of current research progress on the emulsifying capacity and stability of potato proteins and peptides, discussing research challenges and future perspectives. This paper discusses genetic diversity in potato proteins and various methods for extracting proteins from potatoes, including thermal and acid precipitation, salt precipitation, organic solvent precipitation, carboxymethyl cellulose complexation, chromatography, and membrane technology. It also covers enzymatic hydrolysis for producing potato-derived peptides and methods for identifying potato protein-derived emulsifying peptides. Furthermore, it reviews the influence of factors, such as physicochemical properties, environmental conditions, and food-processing techniques on the emulsifying capacity and stability of potato proteins and their derived peptides. Finally, it highlights chemical modifications, such as acylation, succinylation, phosphorylation, and glycation to enhance emulsifying capacity and stability. This review provides insight into future research directions for utilizing potato proteins as sustainable protein sources and high-value food emulsifiers, thereby contributing to adding value to the potato processing industry.