This thesis examines the radiative transfer of extreme ultra-violet (EUV) lasers in plasmas. Harmonic generation, free electron lasers and plasma-based EUV lasers are first reviewed. The accuracy of the Linford formula used to evaluate amplified spontaneous emission (ASE) is examined. A quantitative discussion of backlighters is presented. The maximum plasma thickness able to be probed using extreme ultraviolet (EUV) and harder (1 keV) x-rays is evaluated. It is shown that at higher plasma temperatures (~ 200 eV), EUV radiation (e.g. photon energy = 89 eV) can probe greater optical depth of plasma than x-ray radiation (e.g. photon energy = 1243 eV). The effect of a seed beam injected into an amplifier plasma medium is investigated. TJ1e variation of plasma refractive index with frequency is investigated using the Kramers-Kronig relationship to check the effect ofhigh absorption or gain in a plasma on EUV light. It is shown that a coherent spectral line transmits through absorbing or amplifying plasmas in a near identical manner to incoherent light.