Sourdough (SD) fermentation is a traditional biotechnological process used to improve the properties of baked goods. Nowadays, SD fermentation is studied for its potential health effects due to the presence of postbiotic-like components, which refer to a group of inanimate microorganisms and/or their components that confer health benefits on the host. Some postbiotic-like components reported in SD are non-viable microorganisms, short-chain fatty acids, bacteriocins, biosurfactants, secreted proteins/peptides, amino acids, flavonoids, exopolysaccharides, and other molecules. Temperature, pH, fermentation time, and the composition of lactic acid bacteria and yeasts in SD can impact the nutritional and sensory properties of bread and the postbiotic-like effect. Many in vivo studies in humans have associated the consumption of SD bread with higher satiety, lower glycemic responses, increased postprandial concentrations of short-chain fatty acids, and improvement in the symptoms of metabolic or gastrointestinal-related diseases. This review highlights the role of bacteria and yeasts used for SD, the formation of postbiotic-like components affected by SD fermentation and the baking process, and the implications of functional SD bread intake for human health. There are few studies characterizing the stability and properties of postbiotic-like components after the baking process. Therefore, further research is necessary to develop SD bread with postbiotic-related health benefits.