I present the results of three distinct, but inter-connected studies of the nature and evolution of the host galaxies of quasars. These three are: i) An HST V-band study of a sample of 17 quasars at z ≈ 0.4, with absolute magnitudes in the range -24 ≥ Mv ≥ -28; ii) An HST rest-frame U-band study of matched subsamples of radio-loud and radio-quiet quasars at z ≈ 1 and z ≈ 2; and iii) A UKIRT K-band imaging study of a sample of ULIRG’s and IR-bright QSO’s A 2-dimensional modelling technique has been developed, and used throughout to disentangle the host galaxies from the nucleardominated UV, optical and infrared images.The first study allows an investigation of host galaxy properties across a decade in quasar luminosity, but at a single...