Moringa oleifera Lam (MO), native to India, is a versatile woody plant in the Moringaceae family. Almost every part of MO is edible, with its leaf (MOL) and seed (MOS) extensively studied for their health benefits and functional properties. MOL and MOS are rich in diverse bioactive compounds that provide antioxidant, antibacterial, anti-diabetic, gut health, and anti-inflammatory effects. Key bioactive extracts, such as MO proteins, MO polysaccharides, and MO polyphenols, have found applications in food processing, particularly in the production of dietary supplements and related products. This paper reviews the latest developments in the application of MOL and MOS as functional foods, focusing on their bioactive compounds, extraction methods, and product applications. It also discusses the current status of using MOL and MOS as food ingredients. Given their broad potential, further research into the bioavailability and safety of these compounds is crucial. The food industry should focus on developing MOL and MOS as high-value food materials to enhance human dietary health.