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The primate visual system is organised and wired in a topological manner. From the eye well into extrastriate visual cortex, a preserved spatial representation of the vi- sual world is maintained across many levels of processing. Diffusion-weighted imaging (DWI), together with probabilistic tractography, is a non-invasive technique for map- ping connectivity within the brain. In this thesis I probed the sensitivity and accuracy of DWI and probabilistic tractography by quantifying its capacity to detect topolog- ical connectivity in the post mortem macaque brain, between the lateral geniculate nucleus (LGN) and primary visual cortex (V1). The results were validated against electrophysiological and histological data from previous studies. Using the methodol- ogy developed in this thesis, it was possible to segment the LGN reliably into distinct subregions based on its structural connectivity to different parts of the visual field represented in V1. Quantitative differences in connectivity from magno- and parvo- cellular subcomponents of the LGN to different parts of V1 could be replicated with this method in post mortem brains. The topological corticocortical connectivity be- tween extrastriate visual area V5/MT and V1 could also be mapped in the post mortem macaque. In vivo DWI scans previously obtained from the same brains have lower resolution and signal-to-noise because of the shorter scan times. Nevertheless, in many cases, these yielded topological maps similar to the post mortem maps. These results indicate that the preserved topology of connection between LGN to V1, and V5/MT to V1, can be revealed using non-invasive measures of diffusion-weighted imaging and tractography in vivo. In a preliminary investigation using Human Connectome data obtained in vivo, I was not able to segment the retinotopic map in LGN based on con- nections to V1. This may be because information about the topological connectivity is not carried in the much lower resolution human diffusion data, or because of other methodological limitations. I also investigated the mechanisms of perceptual learning by developing a novel task-irrelevant perceptual learning paradigm designed to adapt neuronal elements early on in visual processing in a certain region of the visual field. There is evidence, although not clear-cut, to suggest that the paradigm elicits task- irrelevant perceptual learning, but that these effects only emerge when practice-related effects are accounted for. When orientation and location specific effects on perceptual performance are examined, the largest improvement occurs at the trained location, however, there is also significant improvement at one other 'untrained' location, and there is also a significant improvement in performance for a control group that did not receive any training at any location. The work highlights inherent difficulties in inves- tigating perceptual learning, which relate to the fact that learning likely takes place at both lower and higher levels of processing, however, the paradigm provides a good starting point for comprehensively investigating the complex mechanisms underlying perceptual learning.