Hypertension and heart failure (HF) are common diseases that, despite advances in medical therapy, continue to be associated with high morbidity and mortality. Therefore, innovative therapeutic strategies are needed. Inhibition of the neutral endopeptidase (NEPinh) had been investigated as a potential novel therapeutic approach because of its ability to increase the plasma concentrations of the natriuretic peptides (NPs). Indeed, the NPs have potent natriuretic and vasodilator properties, inhibit the activity of the renin–angiotensin–aldosterone system, lower sympathetic drive, and have antiproliferative and antihypertrophic effects. Such potentially beneficial effects can be theoretically achieved by the use of NEPinh. However, studies have shown that NEPinh alone does not result in clinically meaningful blood pressure-lowering actions. More recently, NEPinh has been used in combination with other cardiovascular agents, such as angiotensin-converting enzyme inhibitors, and antagonists of the angiotensin receptor. Another future possible combination would be the use of NEPinh with NPs or their newly developed chimeric peptides. This review summarizes the current knowledge of the use and effects of NEPinh alone or in combination with other therapeutic agents for the treatment of human cardiovascular disease such as HF and hypertension.