Neprilysin (NEP), a zinc-dependent membrane-bound metallopeptidase, regulates various bioactive peptides, particularly in kidneys, vascular endothelium, and the central nervous system. NEP's involvement in metabolizing natriuretic peptides, insulin, and enkephalins makes it a promising target for treating cardiovascular and Alzheimer's diseases. Several NEP inhibitors, such as sacubitril and omapatrilat, have been approved for clinical use, which inhibit NEP activity to prolong the bioactivity of beneficial peptides, thereby exerting therapeutic effects. However, despite the broad clinical application prospects of NEP inhibitors, they still have specific adverse reactions and side effects, such as hypotension, renal impairment, and a potentially increased risk of Alzheimer's disease. This manuscript comprehensively reviews the progress on single-target and dual-target NEP inhibitors. Dual-target inhibitors often combine with other therapeutic targets, such as angiotensin receptors, to enhance therapeutic effects and reduce adverse reactions. The article also emphasizes these inhibitors' design strategies, structure-activity relationships (SAR), safety, and clinical performance.