Bovine colostrum (BC) is the initial mammary secretion after parturition, which is nature’s bountiful source consisting of nutritional and bioactive components present in a highly concentrated low-volume format. All mammalian newborns require colostrum to enhance physiological processes such as lifelong immunity, gastrointestinal development, and resistance to microbial infections. The genetic, environmental, and processing methods can all have an impact on the biochemical contents of BC and its supplements. BC and its derivatives have been intensively researched for their potential use in functional foods, medicines, and animal feed. Evidence from clinical studies suggests that BC products are well-tolerated, nontoxic, and safe for human ingestion. Functional foods, feed, and pharmaceutical formulations based on bovine colostrum are playing noteworthy roles in the development of innovative products for promoting health and the prevention of chronic illnesses. This systematic review sheds light on recent research on (a) the effects of processing techniques on BC components, (b) emerging techniques used in the isolation and identification of novel components, (c) BC-based functional foods for human consumption and animal feed supplements, and (d) the role of BC in current drug delivery, as well as future recommendations.