Vegetables represent pillars of good nutrition since they provide important phytochemicals such as fiber, vitamins, antioxidants, as well as minerals. Biofortification proposes a promising strategy to increase the content of specific compounds. As minerals have important functionalities in the human metabolism, the possibility of enriching fresh consumed products, such as many vegetables, adopting specific agronomic approaches, has been considered. This review discusses the most recent findings on agronomic biofortification of vegetables, aimed at increasing in the edible portions the content of important minerals, such as calcium (Ca), magnesium (Mg), iodine (I), zinc (Zn), selenium (Se), iron (Fe), copper (Cu), and silicon (Si). The focus was on selenium and iodine biofortification thus far, while for the other mineral elements, aspects related to vegetable typology, genotypes, chemical form, and application protocols are far from being well defined. Even if agronomic fortification is considered an easy to apply technique, the approach is complex considering several interactions occurring at crop level, as well as the bioavailability of different minerals for the consumer. Considering the latter, only few studies examined in a broad approach both the definition of biofortification protocols and the quantification of bioavailable fraction of the element.