Heavy metal contamination of natural rivers and wastewaters is a problem for both the environment and human society. The accumulation and adsorption of heavy metals could happen with several organic and inorganic matters, but the most used adsorbents are (biological and chemical) organic compounds. This review article presents the basics of heavy metal adsorption on several organic surfaces. There are many organic matters, which seem to be useful as agents for heavy metal adsorption. All of the cited authors and articles present the adsorption kinetics by the most used isotherm models (such as Langmuir and Freundlich isotherms). By comparing several research results presented by a pre-selected assortment of papers, we would like to give an overview of the microbiological, organic chemical, and other surface adsorption possibilities. We draw conclusions for two new adsorption fields (adsorption with biosorbent and artificial materials). We present an optional possibility to study adsorption kinetics, efficiency and regeneration methods to successfully conclude the heavy metal treatment process, and we make some recommendations about the efficient water usage calculations using the water allowance coefficient (WAC) indicator.