Soil quality is seriously reduced due to chemical pollution, including heavy metal (HM) pollution. To meet quality standards, polluted soils must be remediated. Soil washing/soil flushing offers efficient removal of heavy metals and decreases environmental risk in polluted areas. These goals can be obtained by using proper washing agents to remove HMs from soil. These washing agents should not pose unacceptable threats to humans and ecosystems, including soil composition. Currently, it is desirable to use more environmentally and economically attractive washing agents instead of synthetic, environmentally problematic chemicals (e.g., ethylenediaminetetraacetic acid (EDTA)). The usefulness of novel washing agents for treatment of heavy metal-contaminated soils is being intensively developed, in terms of the efficiency of HM removal and properties of washed soils. Despite the unquestionable effectiveness of soil washing/flushing, it should be remembered that both methods generate secondary fluid waste (spent washing solution), and the final stage of the process should be treatment of the contaminated spent washing solution. This paper reviews information on soil contamination with heavy metals. This review examines the principles and status of soil washing and soil flushing. The novel contribution of this review is a presentation of the sources and characteristics of novel washing agents and chemical substitutes for EDTA, with their potential for heavy metal removal. Methods for treating spent washing solution are discussed separately.