The work presented in this doctoral thesis employs colloidal suspensions to explore key open problems in condensed matter physics. Colloidal suspensions, along with gels, polymers, emulsions and liquid crystals belong to a family of materials that are collectively labelled as soft matter. Compositionally, colloidal suspensions consist of particles whose size ranges from a few nanometers to a few microns, dispersed in a solvent. A hallmark feature of these systems is that they exhibit Brownian motion, which makes them suitable for investigating statistical mechanical phenomena. Over the last fifteen years or so, colloids have been used extensively as model systems to shed light on a wide array of such phenomena typically observed in atomic systems. The chief reason why colloids are good mimics of atomic systems is their large size and slow dynamics. Unlike atomic systems, the dynamics of colloids can be probed in real time with single-particle resolution, which allows one to establish the link between macroscopic behavior and the microscopic processes that give rise to it. Yet another important feature is that colloidal systems exhibit various phases of matter such as crystals, liquids and glasses, which makes them versatile model systems that can probe a broad class of condensed matter physics problems. The work described in this thesis takes advantage of these lucrative features of colloidal suspensions to gain deeper insights into the physics of glass formation as well as shear-induced anisotropic grain growth in polycrystalline materials. The thesis is organized into two preliminary chapters, four work chapters and a concluding chapter, as follows. Chapter 1 provides an introduction to colloidal suspensions and reviews the chief theo-retical concepts regarding glass formation and grain boundary dynamics that form an integral part of subsequent chapters. Chapter 2 describes the experimental methods used for performing the work presented in the thesis and consists of two parts. The first part describes the protocols followed for synthesizing the size-tunable poly (N-isoprolypacrylamide) (PNIPAm) particles used in our study of shear-induced grain growth. The second part describes the instrumentation and techniques, such as holographic optical tweezers, confocal microscopy, rheology and Bragg diffraction microscopy, used to perform the measurements described in the thesis. Chapter 3 deals with our work on the dynamical facilitation (DF) theory of glass forma-tion. Despite decades of research, it remains to be established whether the transformation of a liquid into a glass is fundamentally thermodynamic or dynamic in origin. While obser-vations of growing length scales are consistent with thermodynamic perspectives, the purely dynamic approach of the DF theory has thus far lacked experimental support. Further, for glass transitions induced by randomly freezing a subset of particles in the liquid phase, theory and simulations support the existence of an underlying thermodynamic phase transi-tion, whereas the DF theory remains unexplored. In Chapter 3, using video microscopy and holographic optical tweezers, we show that dynamical facilitation in a colloidal glass-forming liquid grows with density as well as the fraction of pinned particles. In addition, we observe that heterogeneous dynamics in the form of string-like cooperative motion, which is consid-ered to be consistent with thermodynamic theories, can also emerge naturally within the framework of facilitation. These findings suggest that a deeper understanding of the glass transition necessitates an amalgamation of existing theoretical approaches. In Chapter 4, we further explore the question of whether glass formation is an intrinsi-cally thermodynamic or dynamic phenomenon. A major obstacle in answering this question lies in determining whether relaxation close to the glass transition is dominated by activated hopping, as espoused by various thermodynamic theories, or by the correlated motion of localized excitations, as proposed in the Dynamical Facilitation (DF) approach. In Chapter 4, we surmount this central challenge by developing a scheme based on real space micro-scopic analysis of particle dynamics and applying it to ascertain the relative importance of hopping and facilitation in a colloidal glass-former. By analysing the spatial organization of excitations within cooperatively rearranging regions (CRRs) and examining their parti-tioning into shell-like and core-like regions, we establish the existence of a crossover from a facilitation-dominated regime at low area fractions to a hopping-dominated one close to the glass transition. Remarkably, this crossover coincides with the change in morphology of CRRs predicted by the Random First-Order Transition theory (RFOT), a prominent ther-modynamic framework. Further, we analyse the variation of the concentration of excitations with distance from an amorphous wall and find that the evolution of these concentration profiles with area fraction is consistent with the presence of a crossover in the relaxation mechanism. By identifying regimes dominated by distinct dynamical processes, our study offers microscopic insights into the nature of structural relaxation close to the glass transi-tion. In Chapter 5, we extend our investigation of the glass transition to systems composed of anisotropic particles. The primary motivation for this is to bridge a long-standing di-vide between theories and simulations on one hand, and experiments on molecular liquids on the other. In particular, theories and simulations predominantly focus on simple glass-formers composed of spherical particles interacting via isotropic interactions. Indeed, even the prominent theory of Dynamical Facilitation has not even been formulated to account for anisotropic shapes or interactions. On the other hand, an overwhelming majority of liquids possess considerable anisotropy, both in particle shape as well as interactions. In Chapter 5, we mitigate this situation by developing the DF theory further and applying it to systems with orientational degrees of freedom as well as anisotropic attractive interactions. By analyzing data from experiments on colloidal ellipsoids, we show that facilitation plays a pivotal role in translational as well as orientational relaxation. Further, we demonstrate that the introduction of attractive interactions leads to spatial decoupling of translational and rotational facilitation, which subsequently results in the decoupling of dynamical het-erogeneities. Most strikingly, the DF theory can predict the existence of reentrant glass transitions based on the statistics of localized dynamical events, called excitations, whose duration is substantially smaller than the structural relaxation time. Our findings pave the way for systematically testing the DF approach in complex glass-formers and also establish the significance of facilitation in governing structural relaxation in supercooled liquids. In Chapter 6, we turn our attention away from the glass transition and address the problem of grain growth in sheared polycrystalline materials. The fabrication of functional materials via grain growth engineering implicitly relies on altering the mobilities of grain boundaries (GBs) by applying external fields. While computer simulations have alluded to kinetic roughening as a potential mechanism for modifying GB mobilities, its implications for grain growth have remained largely unexplored owing to difficulties in bridging the disparate length and time scales involved. In Chapter 6, by imaging GB particle dynamics as well as grain network evolution under shear, we present direct evidence for kinetic roughening of GBs and unravel its connection to grain growth in driven colloidal polycrystals. The capillary fluctuation method allows us to quantitatively extract shear-dependent effective mobilities. Remarkably, our experiments reveal that for sufficiently large strains, GBs with normals parallel to shear undergo preferential kinetic roughening resulting in anisotropic enhancement of effective mobilities and hence directional grain growth. Single-particle level analysis shows that the anisotropy in mobility emerges from strain-induced directional enhancement of activated particle hops normal to the GB plane. Finally, in Chapter 7, we present our conclusions and discuss possible future directions.