Mozzarella cheese is a white, lightly flavored, stretchable cheese produced through a hot-stretching process, which endows the product with unique functional properties such as stretchability and meltability. Stretchability is defined as the ability of the cheese to form long, thin bundles of fibers without breaking, and it is a critical quality characteristic of Mozzarella cheese and also an important indicator for quality evaluation, determining its marketability and price. This paper delves into the formation mechanism of stretchability in Mozzarella cheese and outlines the factors affecting it such as the content and structure of casein micelles (including particle size and monomer composition), the content and forms of calcium ions, the size of milk fat globules, and blanching and stretching conditions (acidification, blanching, and stretching). The relationship between nutrient contents of raw milk and cheese stretchability is also discussed. This review provides theoretical guidance for the development and utilization of milk resources in China and offers a scientific basis for the production of Mozzarella cheese with excellent stretching characteristics. Furthermore, a brief analysis is made of the current situation and problems of Mozzarella cheese production in China in order to provide a reference for the development of the Mozzarella cheese industry.