Biosorption is a variant of sorption techniques in which the sorbent is a material of biological origin. This technique is considered to be low cost and environmentally friendly, and it can be used to remove pollutants from aqueous solutions. The objective of this review is to report on the most significant recent works and most recent advances that have occurred in the last couple of years (2019–2020) in the field of biosorption. Biosorption of metals and organic compounds (dyes, antibiotics and other emerging contaminants) is considered in this review. In addition, the use and possibilities of different forms of biomass (live or dead, modified or immobilized) are also considered.