This review summarises the methods currently available to extract radioactive actinide elements from solutions of spent nuclear fuel. This separation of actinides reduces the hazards associated with spent nuclear fuel, such as its radiotoxicity, volume and the amount of time required for its' radioactivity to return to naturally occurring levels. Separation of actinides from environmental water systems is also briefly discussed. The actinide elements typically found in spent nuclear fuel include uranium, plutonium and the minor actinides (americium, neptunium and curium). Separation methods for uranium and plutonium are reasonably well established. On the other hand separation of the minor actinides from lanthanide fission products also present in spent nuclear fuel is an ongoing challenge and an area of active research. Several separation methods for selective removal of these actinides from spent nuclear fuel will be described. These separation methods include solvent extraction, which is the most commonly used method for radiochemical separations, as well as the less developed but promising use of adsorption and ion-exchange materials. Crown Copyright (C) 2016 Published by Elsevier B.V. All rights reserved.