Hard rod and plate particles have previously shown an interesting range of liquid crystalline phase behaviour in experiments, simulation and theory. Under certain conditions a biaxial phase has been proposed but this has not been shown experimentally yet. The phase behaviour of hard rods in a non-aqueous solvent was studied in the first experimental chapter. Onsager theory predicts an isotropic-nematic transition for infinitely long, thin rods. In practice colloidal rods have a finite aspect ratio and it is shown that the midpoint of the coexistence boundaries agree well with computer simulations. The width of the transition, however, is increased noticeably due to polydispersity in aspect ratio and this is found to be in broad agreement with theoretical predictions for infinitely thin, polydisperse rods. The second experimental chapter of this thesis showed that it is possible to adsorb sodium polyacrylate on to the clay surface of sepiolite clay rods in order to electrostatically stabilise the particles in water. It was possible to disrupt the formation of a gel phase and observe isotropic - nematic phase behaviour. The isotropic - nematic phase boundaries increased with salt concentration. The final chapters of this thesis investigated mixtures of rod and plate particles. Firstly aqueous sepiolite rods stabilised with sodium polyacrylate were mixed with various concentrations of montmorillonite plates. For low concentrations of the plates, the sepiolite underwent phase separation as previously seen but at a much lower rod concentration with a broader coexistence range. It was found that it was possible to obtain 3 phases in coexistence for a number of samples but the montmorillonite-rich phase, despite observations of slight birefringence, was not considered a nematic. Yet, the montmorillonite-rich phase did contain a higher concentration of particles than seen in the pure samples. Lastly mixtures of sepiolite rods and gibbsite plates in both aqueous and non-aqueous solvents were explored. It was found in both cases that the opposite charge on the particles led to gelation of the particles which inhibited any demixing. For the aqueous system it was found that adsorption of sodium poly acrylate to the surface of the gibbsite particles was able to reverse the sign of the particle which reSUlting in a stable dispersion of the rod and plate particles similar to that seen for the mixtures of sepiolite and montmorillonite.