This review describes experimental results demonstrating amplification of XUV radiation at discreet wavelengths between 8.1 nm and 18.2 nm. The amplifying medium is generated by recombination in expanding, laser-heated thin fibre targets. Gain coefficients between 1-5 cm-1 have been observed in transitions in hydrogenic (CVI and FIX) and Li-like (AlXI) ions. The work has been carried out using the VULCAN laser of the SERC Central Laser Facility at the Rutherford-Appleton Laboratory and is the product of national and international collaborations.