Plant-based diets are becoming more popular for many reasons, and epidemiological as well as clinical data also suggest that a well-balanced vegan diet can be adopted for the prevention, and in some cases, in the treatment of many diseases. In this narrative review, we provide an overview of the relationships between these diets and various conditions and their potential biochemical background. As whole plant foods are very rich in food-derived antioxidants and other phytochemicals, they have many positive physiological effects on different aspects of health. In the background of the beneficial health effects, several biochemical processes could stand, including the reduced formation of trimethylamine oxide (TMAO) or decreased serum insulin-like growth factor 1 (IGF-1) levels and altered signaling pathways such as mechanistic target of rapamycin (mTOR). In addition, the composition of plant-based diets may play a role in preventing lipotoxicity, avoiding N-glycolylneuraminic acid (Neu5Gc), and reducing foodborne endotoxin intake. In this article, we attempt to draw attention to the growing knowledge about these diets and provide starting points for further research.