The results of two studies of M31's globular cluster system are presented. One study used deep V- and I-band images of 24 M31 globular clusters taken with CFHT's HRCam. This data is the best available ground-based data for determining structural parameters (such as core and tidal radii, ellipticities, and orientations) for M31's globular clusters. Two-dimensional Michie-King models were fit to each cluster and the results compared to the structural parameters of the Galactic clusters. There is no evidence for any difference between the mean tidal radii and ellipticities of globular clusters in the two galaxies. Core radii and half-mass radii are too strongly affected by seeing to allow a comparison between the two galaxies. The second study used deep HST WFC V- and I-band images of G302 and G312, two globular clusters in M31's halo, to obtain the deepest colour-magnitude diagrams of any M31 globular cluster. Structural parameters were determined for the two clusters and compared to those from the CFHT data. Tidal radii and ellipticities from the CFHT data agree with the more reliable results obtained from HST data. The core radii agree for seeings of ≾ 4 times the cluster's core radius. It is not possible to obtain reliable core parameters for the M31 clusters using ground-based telescopes unless adaptive optics are used to reduce the seeing to ≾ 0”.1. However, the overall sizes and shapes of the clusters can easily be measured if FWHM ≾ 1". Images of M31 clusters obtained from the ground have similar resolutions to those of Virgo globular clusters obtained with the HST's PC. Therefore detailed structural parameters can be obtained for globular clusters in the elliptical galaxies of the Virgo cluster. This thesis also presents the deepest colour-magnitude diagram for M31's halo. There is no evidence for young stars, or of a second parameter problem in M31's halo. The halo stars have [m/H] ~ -0.6 with a spread of -2.0 ≾ [m/H] ≾ -0.2. The M31 halo is ~ 8 times more metal-rich than the Galactic halo and ~ 4 times more metal-rich than the M31 globular cluster system. [Scientific formulae used in this abstract could not be reproduced.]