The passive removal of toxic heavy metals such as Cd(2+), Cu(2+), Zn(2+), Pb(2+), Cr(3+), and Hg(2+) by inexpensive biomaterials, termed biosorption, requires that the substrate displays high metal uptake and selectivity, as well as suitable mechanical properties for applied remediation scenarios. In recent years, many low-cost sorbents have been investigated, but the brown algae have since proven to be the most effective and promising substrates. It is their basic biochemical constitution that is responsible for this enhanced performance among biomaterials. More specifically, it is the properties of cell wall constituents, such as alginate and fucoidan, which are chiefly responsible for heavy metal chelation. In this comprehensive review, the emphasis is on outlining the biochemical properties of the brown algae that set them apart from other algal biosorbents. A detailed description of the macromolecular conformation of the alginate biopolymer is offered in order to explain the heavy metal selectivity displayed by the brown algae. The role of cellular structure, storage polysaccharides, cell wall and extracellular polysaccharides is evaluated in terms of their potential for metal sequestration. Binding mechanisms are discussed, including the key functional groups involved and the ion-exchange process. Quantification of metal-biomass interactions is fundamental to the evaluation of potential implementation strategies, hence sorption isotherms, ion-exchange constants, as well as models used to characterize algal biosorption are reviewed. The sorption behavior (i.e., capacity, affinity) of brown algae with various heavy metals is summarized and their relative performance is evaluated.