In this work I model the liquid crystal polymers as worms and explore the Spheroidal approach to examine their statistical mechanics. Several models are presented in this work to describe main chain-, side chain-polymers, polymer networks and gels in their nematic state. In the case of main chain nematic polymers, the worm flexibility, favouring disorder, and the nematic potential, tending to align segments to be parallel to each other, compete to determine the properties of polymers. I predict the temperature dependence of order parameter and phase transition behaviour for different lengths of the polymers, and the dimensions as well. Subsequently, I examine the critical features of the nematic polymer when an electrical field is applied. Side chain polymers with semi-flexible backbone and stiff nematogenic pendants form interesting nematic phases, largely as a consequence of competition between backbone entropy and pendant order. I classify them into three categories: NI, NII, and NIII phase, according to volume fractions, temperature, nematic coupling constants, and stiffness. In these phases the backbone and pendants have orders different in magnitude and/or in sign in order to achieve a stable state. Phase diagrams are given. In addition, I predict unusual properties such as anomalous temperature variation of optical anisotropy and molecular conformational changes. Crosslinks confine polymer chains in a network so that their strands have a shape different from their natural ones. Such constraints shift phase transition temperature. The other effect is that crosslinks give the system rubber elasticity. Combining rubber elasticity with liquid crystal features, networks exhibit unusual phenomena, such as discontinuous stress-strain relations, spontaneous shape changes, non-linear stress-optical laws and deviations from classical behaviour of conventional elastomers. It is proposed that residual nematic interaction is responsible for deviations found in classical elastomers. The nematic networks swollen by isotropic solvent form nematic gels. At low temperatures a nematic gel coexists with excess solvent, at high temperatures the coexisting gel is isotropic. In addition, coexistence is predicted between nematic and isotropic gels. There is an associated triple point. There are possible elastic problems associated with different phases coexisting in one gel sample. Main chain nematic polymers have been modelled either as homogeneous worms, or as jointed rods by others. In reality the polymers are composed of the mesogens linked by semi-flexible spacers. One must expect that the spacers have an order differing from the mesogens. The consecutive mesogens are not decoupled and the spacers are able to talk to each other via the mesogens in between. The model presented takes account of molecular parameters, such as length of the mesogen and spacer, and their interactions. The nematic order of the two components, the nematic-isotropic transition, and dimensions of the polymers are addressed. Finally, I examine both worm and jointed rod models, to see when each is applicable. Accordingly an elastically jointed rod model is presented. Hairpins, found naturally in the worm problem, also exist for jointed systems but their scaling is quite different. Comparisons of these results with experiments are accordingly made and are found to be satisfactory.

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