Food protein-derived bioactive peptides are recognized as valuable ingredients of functional foods and/or nutraceuticals to promote health and reduce the risk of chronic diseases. However, although peptides have been demonstrated to exert multiple benefits by biochemical assays, cell culture, and animal models, the ability to translate the new findings into practical or commercial uses remains delayed. This fact is mainly due to the lack of correlation of in vitro findings with in vivo functions of peptides because of their low bioavailability. Once ingested, peptides need to resist the action of digestive enzymes during their transit through the gastrointestinal tract and cross the intestinal epithelial barrier to reach the target organs in an intact and active form to exert their health-promoting properties. Thus, for a better understanding of the in vivo physiological effects of food bioactive peptides, extensive research studies on their gastrointestinal stability and transport are needed. This review summarizes the most current evidence on those factors affecting the digestive and absorptive processes of food bioactive peptides, the recently designed models mimicking the gastrointestinal environment, as well as the novel strategies developed and currently applied to enhance the absorption and bioavailability of peptides.