More than one billion people worldwide suffer from hypertension, and essential arterial hypertension is in particular a major risk factor for cardiovascular diseases. These conditions can lead to complications such as stroke, renal failure, cardiac hypertrophy, and heart failure. Despite extensive research on various antihypertensive drugs, an increasing number of people are unable to effectively control their hypertension. Further optimization of their treatment is required. Given the pathogenesis of hypertension, natural products (NPs) have emerged as a promising source of potential antihypertensive agents. NPs can prevent the development of hypertension by targeting oxidative stress, inflammation, vascular remodeling, and neurohormonal pathways. These targets provide the foundation for the application of NPs in clinical treatment. This review assesses NPs with potential antihypertensive activities published between 2019 and 2024. A total of 70 unique NPs were identified through PubMed and Web of Science. Seventy unique NPs were categorized into flavonoids (20 compounds), terpenoids (24 compounds), alkaloids (17 compounds), and plant-derived extracts (9 species). These products were classified according to their structural frameworks, and their bioactivities were briefly summarized. Future research should prioritize NPs with dual anti-oxidant/anti-inflammatory properties for clinical experiments, advanced delivery systems for improved bioavailability, and interdisciplinary approaches integrating synthetic biology for scalable production.