Human micronutrient deficiencies are a widespread problem worldwide and mainly concern people whose diet (mainly of plant origin) consists of insufficient amounts of critical vitamins and minerals. Low levels of micronutrients in plants are linked to, i.e., their decreasing concentration in soils and/or low bioavailability and presence of abiotic stresses which disturb the proper growth and development of plants. Agronomic biofortification of crops is a very promising way to improve the concentration of micronutrients in edible parts of crops without compromising yield and is recognized as the cheapest strategy to alleviate hidden hunger worldwide. The review is focused on the factors influencing the effectiveness of biofortified crops (a type of application, form, and a dose of applied microelement, biofertilizers, and nanofertilizers). Also, the accumulation of zinc, selenium, and iron in edible parts of crops, their effects on metabolism, morphological and yield parameters, and an impact on plants’ defense mechanisms against abiotic stress like salt, high/low temperature, heavy metal, and drought was discussed. Finally, the directions of future agronomic biofortification studies are proposed.