The design, construction and operation of advanced divertors have been themain topics of tokamak research during the last decade. The design ofthese divertors (carried out with two-dimensional plasma modelling codes)has been optimized to provide: a large operating density range forpartially detached plasmas with large radiative losses; satisfactoryparticle control by efficient deuterium pumping; and He exhaust capabilitysufficient to remove fusion ashes when extrapolated to next step devices.This article explains the criteria that have guided this optimizationprocess and then critically reviews the experimental evidence thatconfirms or refutes the physics-based design criteria on which the variousexisting advanced divertors have been based.