Colloidal suspensions are ubiquitous in consumer products and industry, but the details of how particle structures and interactions lead to their macroscopic properties are often not well understood. In this thesis, we show methods for using shear or compression to modify the microstructure of colloidal suspensions and relate these modifications to system-scale changes. In colloidal gels, we investigate the use of oscillatory shear protocols to embed a memory of the applied shear. This method is able to modify the yield strain of the gel without changing any of the constituent components or interactions. By combining our shear protocols with confocal microscopy, we are able to identify which particles in the gel are rearranging the most and correlate these changes with a lower number of neighboring particles. Analysis of the local microstructure also reveals that the bond angle distribution remains isotropic even as the gel structures rearrange to support increased strains. This lack of directionality in the gel bond structure helps explain the other main finding of our gel experiments: when trained along one axis, the same shear memory can be measured along an orthogonal axis. Our study of colloidal glasses utilizes a similar combination of macroscopic manipulation and confocal microscopy to investigate the Gardner transition. The Gardner transition is a critical phase transition occurring deep within the glass phase where glass states break into a multitude of marginally stable states with vanishingly small energy barriers between them. In our three-dimensional glass, the Gardner phase is expected to emerge as caged glass particles become trapped in subcages of their neighbors. We apply cycles of compression to a colloidal glass and track particle positions and cage properties over time to look for the signatures of the Gardner transition. This study is one of the first experimental explorations of marginal states in a three-dimensional glass and can help to clarify the nature and characteristics of the Gardner transition in physical dimensions. Together, these experiments on colloidal gels and glasses provide insight into the local microstructural changes that occur as colloidal suspensions are subjected to macroscopic manipulations.