Lactic acid bacteria (LAB) and propionic acid bacteria (PAB) are widely used in the manufacture of cheeses and other fermented dairy products. Bacterial species used as starters are mainly chosen according to their intrinsic properties: the milk acidifying capacity for LAB starters and the aromatizing properties of PAB, for example. Beyond the general characteristics of a bacterial species, many key phenotypic traits determining their interest for dairy applications depend on the strain within a given species. Through some examples, this review illustrates how the choice of a bacterial strain with specific technological characteristics, within a given species of LAB or PAB, can determine the final properties in the end product. This concerns the technological properties of cheeses, such as flavour, texture, and opening formation, and their functional properties, such as inhibition of undesirable microorganisms and health properties. When known, the genetic determinants of the diversity are presented. This review emphasizes the importance of preserving and exploring microbial resources at the intraspecific level, as an unending source of diversity for innovation in food fermentation.