The numerous physiological functions of the nonessential amino acid L-aspartate, the semi-essential amino acid L-arginine, and the essential amino acid L-lysine, made them attractive for a wide range of nutritional and/or therapeutic applications. Furthermore, the administration of these amino acids as mixtures or as dipeptides for higher bioavailability is scientifically approved, and various commercial products of these forms are already available on the market. Although the industrial production of dipeptides is, with few exceptions, in an early stage, several strategies have been established and are compared in this review. Additionally, the recent developments in the technical production of aspartate-arginine and aspartate-lysine dipeptides from the biopolymer cyanophycin produced in microorganisms are discussed. Cyanophycin-derived dipeptides are produced exclusively by biotechnological procedures, probably possess higher bioavailability and may be used as better alternatives to the widely applied amino acid mixtures. Thus, the pivotal advantages and the potential applications of these dipeptides as well as of their constituting amino acids in nutrition and therapy are also discussed. Special emphasis is dedicated to arginine due to its numerous physiological roles in many cardiovascular, genitourinary, gastrointestinal, and immune disorders.