Abstract Biosorption is an extensively studied technology applied for the removal of heavy metal ions and other pollutants from aqueous solutions. Most biosorption research is focused on the experimentally measured sorption isotherms, kinetics and thermodynamics. The aim of this paper is to review a class of theoretical models developed for the interpretation of such experimental data related to biosorption of metal cations by alginate-containing sorbents (e.g. algal biosorbents). The focus is put on: (i) modeling the biosorption equilibrium isotherms (including the description of the pH and ionic strength effects); (ii) thermodynamics of biosorption; (iii) kinetics of biosorption; and (iv) metal ion binding modes. This review facilitates the choice of the model suitable for the given type of data and describes the most common mistakes made during the data analysis (e.g. the use of incorrect or oversimplified models).