I have studied the effects of polydispersity on the phase behaviour of suspensions of PMMA colloidal spheres on their own and in the presence of non-adsorbed polymer. I systematically explored the volume fraction-polydispersity phase behaviour of hard spheres (with radii R =167, 244, 300 and 303nm) through direct observations and crystallography measurements. I observed normal crystallisation for sigma < 7:5%, and no crystals at sigma > 18%. Samples at sigma ~~ 9.5% showed crystal-fluid coexistence between 0:52 < phi < 0:56 but no fully crystalline be- haviour above this region. This may be explained by slow particle diffusion in the dense metastable fluid and a glass transition, possibly involving only the larger particles. The addition of random coil polymer (radius of gyration rg) to a suspension of single-sized spherical colloidal particles induces an attractive depletion potential which, for size ratios Xi = rg=R < 0:2, has the effect of expanding the crystal-fluid coexistence region. Surprisingly, when such a polymer solution (with Xi = 0:1), with a range of concentrations cp, is added to a polydisperse colloidal suspension (sigma ~~ 10%), crystal formation is actually suppressed. This can be explained by the fact that the polymer compresses the nascent crystal phase to volume fractions greater than the maximum phi permitted for polydisperse spheres. By modifying existing free energy equations to include the effects of colloidal polydispersity we also succeed in reproducing the observed phase diagram. Larger added polymer (Xi > 0:3) introduces a region of stable gas-liquid coexistence. In systems where crystallisation is suppressed due to polydispersity, this will theoretically be the only transition. By preparing many samples over a range of phi and cp this prediction was observed experimentally for Xi = 0:5. Fractionation studies on coexisting phases enabled verification of a recent universal law of fractionation in slightly polydisperse systems.