Adsorption operations are widely used in the process industry for the purification and bulk separation of gaseous and liquid mixtures. In the last decades, such separation processes also played an important role in renal and liver replacement therapy. This chapter presents a short overview of the main aspects related to adsorption processes. In consideration of the specific scope of this book, only purification of liquid diluted systems, i.e. adsorption of one or more diluted species from a liquid solution, are covered. Furthermore, since in most applications adsorption is carried out in fixed bed columns, the chapter is focused on this operating mode. A particular emphasis is put on the use of mathematical models as a tool for gaining a deeper insight into the working principles and operation of adsorption units embedded in artificial organs.