This chapter is focused on the design of artificial liver support devices (LSD). After a short overview of liver functions and pathologies, aimed at defining the minimum requirements for artificial devices, a survey of the different artificial liver support devices developed and used in clinical practice is reported. Subsequently, starting from a description of the physicochemical phenomena that characterize each unit operation used in the detoxification process (albumin dialysis and toxin adsorption), mathematical models of dialysis and adsorption units are developed and combined into an LSD model. A proposal for a first approach to a patient-device model is also considered to predict the evolution in time of toxin levels in patient blood and to evaluate the effectiveness of the treatment. The chapter ends with a survey on the bio-artificial liver devices.