This Thesis presents a study of the nature and evolution of far-infrared (FIR) luminous galaxies using sources selected at 70 μm from the Spitzer Wide-area InfraRed Extragalactic (SWIRE) Survey. The SWIRE survey was the largest of the legacy surveys conducted by the Spitzer Space Telescope covering 49 deg² in six fields. The nature of the FIR sources was explored by obtaining spectroscopic follow-up observations of 70 μm sources selected from the SWIRE Lockman Hole (LH) and XMM-LSS fields. The observations were carried out at the William Herschel Telescope (WHT) using the multi-object spectrograph AF2/WYFFOS. The data were first reduced and calibrated using standard IRAF routines and redshifts measured by identifying emission and absorption lines. The data reduction and redshift measurement steps are described in detail. The spectra were then used to determine the optical and IR properties of 70 μm sources by performing emission line diagnostic and modelling the multiwavelength spectral energy distribution (SED) for these objects. The evolution of FIR luminous galaxies is investigated by constructing 70 and 160 μm and total IR (TIR) luminosity functions (LFs) for all 70 and 160 μm sources in SWIRE LH and XMM-LSS with a measured spectroscopic redshift. In this work the evolution of the 70 μm and TIR LFs was investigated to redshift, z = 1.2, and the evolution of the 160 μm LF was computed to z = 0.5. The final work, was carried out by including 70 and 160 μm sources with photometric redshifts and studying the evolution of FIR luminous galaxies to z = 2 and z = 1.5 respectively. The evolution of the TIR LF was also determined using the 70 μm sample to z = 2. The work presented in this Thesis utilises, for the first time, a parametric Bayesian method to study the evolution of IR galaxies.