Molecular dynamics simulation performed on modern computer workstations provides a powerful tool for the investigation of the static and dynamic characteristics of liquid crystal phases. In this thesis molecular dynamics computer simulations have been performed for two model systems. Simulations of 4,4'-di-n-pentyl-bibicyclo[2.2.2]octane demonstrate the growth of a structurally ordered phase directly from an isotropic fluid. This is the first time that this has been achieved for an atomistic model. The results demonstrate a strong coupling between orientational ordering and molecular shape, but indicate that the coupling between molecular conformational changes and molecular reorientation is relatively weak. Simulations have also been performed for a hybrid Gay-Berne/Lennard-Jones model resulting in thermodynamically stable nematic and smectic phases. Frank elastic constants have been calculated for the nematic phase formed by the hybrid model through analysis of the fluctuations of the nematic director, giving results comparable with those found experimentally. Work presented in this thesis also describes the parameterisation of the torsional potential of a fragment of a dimethyl siloxane polymer chain, disiloxane diol (HOMe(_2)Si)(_2)O, using ab initio quantum mechanical calculations.