Pollution by heavy metals (HM) represents a serious threat for both the environment and human health. Due to their elemental character, HM cannot be chemically degraded, and their detoxification in the environment mostly resides either in stabilization or in their removal from the matrix, e.g., soil. For this purpose, phytoremediation, i.e., the application of plants for the restoration of a polluted environment, has been proposed as a promising green alternative to traditional physical and chemical methods. Among the phytoremediation techniques, phytoextraction refers to the removal of HM from the matrix through their uptake by a plant. It possesses considerable advantages over traditional techniques, especially due to its cost effectiveness, potential treatment of multiple HM simultaneously, no need for the excavation of contaminated soil, good acceptance by the public, the possibility of follow-up processing of the biomass produced, etc. In this review, we focused on three basic HM phytoextraction strategies that differ in the type of plant species being employed: natural hyperaccumulators, fast-growing plant species with high-biomass production and, potentially, plants genetically engineered toward a phenotype that favors efficient HM uptake and boosted HM tolerance. Considerable knowledge on the applicability of plants for HM phytoextraction has been gathered to date from both lab-scale studies performed under controlled model conditions and field trials using real environmental conditions. Based on this knowledge, many specific applications of plants for the remediation of HM-polluted soils have been proposed. Such studies often also include suggestions for the further processing of HM-contaminated biomass, therefore providing an added economical value. Based on the examples presented here, we recommend that intensive research be performed on the selection of appropriate plant taxa for various sets of conditions, environmental risk assessment, the fate of HM-enriched biomass, economical aspects of the process, etc.