Bovine colostrum (BC), the first milk secreted by mammals after birth, is a trending alternative source for supplementing infants and children, offering benefits for gut and immune health. Its rich components, such as proteins, immunoglobulins, lactoferrin, and glycans, are used to fortify diets and support development. Preterm development is crucial, especially in the maturation of essential systems, and from 2010 to 2020, approximately 15% of all premature births occurred at less than 32 weeks of gestation worldwide. This review explores the composition, benefits, and effects of BC on general infants and children, along with preterm infants who require special care, and highlights its role in growth and development. BC is also associated with specific pediatric diseases, including necrotizing enterocolitis (NEC), infectious diarrhea, inflammatory bowel disease (IBD), short-bowel syndrome (SBS), neonatal sepsis, gastrointestinal and respiratory infections, and some minor conditions. This review also discusses the clinical trials regarding these specific conditions which are occasionally encountered in preterm infants. The anti-inflammatory, antimicrobial, immunomodulatory, and antiviral properties of BC are discussed, emphasizing its mechanisms of action. Clinical trials, particularly in humans, provide evidence supporting the inclusion of BC in formulas and diets, although precise standards for age, feeding time, and amounts are needed to ensure safety and efficacy. However, potential adverse effects, such as allergic reactions to caseins and immunoglobulin E, must be considered. More comprehensive clinical trials are necessary to expand the evidence on BC in infant feeding, and glycans, important components of BC, should be further studied for their synergistic effects on pediatric diseases. Ultimately, BC shows promise for pediatric health and should be incorporated into nutritional supplements with caution.