Generally, bioactive peptides are natural compounds of food or part of protein that are inactive in the precursor molecule. However, they may be active after hydrolysis and can be transported to the active site. Biologically active peptides can also be synthesized chemically and characterized. Peptides have many properties, including antihypertensive, antioxidant, antimicrobial, anticoagulant, and chelating effects. They are also responsible for the taste of food or for the inhibition of enzymes involved in the development of diseases. The scientific literature has described many peptides with bioactive properties obtained from different sources. Information about the structure, origin, and properties of peptides can also be found in many databases. This review will describe peptides inhibiting the development of current diseases, peptides with antimicrobial properties, and new alternative sources of peptides based on the current knowledge and documentation of their bioactivity. All these issues are part of modern research on peptides and their use in current health or technological problems in food production.