The consumption of healthy food, in order to strengthen the immune system, is now a major focus of people worldwide and is essential to tackle the emerging pandemic concerns. Moreover, research in this area paves the way for diversification of human diets by incorporating underutilized crops which are highly nutritious and climate-resilient in nature. However, although the consumption of healthy foods increases nutritional uptake, the bioavailability of nutrients and their absorption from foods also play an essential role in curbing malnutrition in developing countries. This has led to a focus on anti-nutrients that interfere with the digestion and absorption of nutrients and proteins from foods. Anti-nutritional factors in crops, such as phytic acid, gossypol, goitrogens, glucosinolates, lectins, oxalic acid, saponins, raffinose, tannins, enzyme inhibitors, alkaloids, β-N-oxalyl amino alanine (BOAA), and hydrogen cyanide (HCN), are synthesized in crop metabolic pathways and are interconnected with other essential growth regulation factors. Hence, breeding with the aim of completely eliminating anti-nutrition factors tends to compromise desirable features such as yield and seed size. However, advanced techniques, such as integrated multi-omics, RNAi, gene editing, and genomics-assisted breeding, aim to breed crops in which negative traits are minimized and to provide new strategies to handle these traits in crop improvement programs. There is also a need to emphasize individual crop-based approaches in upcoming research programs to achieve smart foods with minimum constraints in future. This review focuses on progress in molecular breeding and prospects for additional approaches to improve nutrient bioavailability in major crops.