Cavitation is a topic that has long been of interest due to the large and growing range of applications associated with it. This is mainly because the collapse of cavitation bubbles releases a considerable amount of energy into the surrounding environment. This release of energy has detrimental consequences in certain applications, but can also be exploited beneficially in others. The fundamental dynamics of the bubble collapse are generally affected by the presence of a nearby boundary and can change depending on the nature of that boundary. In this thesis, we thus investigate the effects of deformable boundaries on the behavior of cavitation bubbles. Specifically, we consider two types of boundaries: a granular boundary and an elastic boundary. We evaluate key features of the bubble behavior through high-speed imaging of laser-induced cavitation bubbles and with a potential flow solver. For both types of boundaries studied, we compare the characteristics of the bubbles to that of similar bubbles that develop near a rigid boundary, an already well-document configuration. The granular boundaries consist of beds of sand composed of spherical soda lime glass beads with varying granularities. In comparison to a rigid boundary, a granular boundary leads to bubbles with shorter lifetimes and reduced centroid displacements. Above gamma = 1.3, the bubble exhibits similar features to that of a bubble near a rigid boundary. However, when gamma is between 0.6 and 1.3, the deformation of the boundary forces the bubble to adopt a conical shape as it collapses, eventually resulting in the formation of micro-jets that are significantly faster than those observed near a rigid boundary at the same stand-off distance. For gamma < 0.6, the bubble develops a bell-shaped form, leading to the formation of thin micro-jets that travel faster than 1000 m/s. Moreover, between gamma = 1.3 and gamma = 0.3, granular jets erupt from the sand surface following the bubble collapse. By replacing the sand with an equivalent liquid, we find that the anisotropy parameter zeta, a dimensionless version of the Kelvin impulse, can be used to predict the displacement of the bubble centroid and its second oscillation period. Using the same assumption, we also find that the potential flow simulations yield fairly accurate predictions of the bubble behavior. The elastic boundaries consist of agarose hydrogels with varying elasticity. Based on the stand-off distance, it is possible to dissociate two main oscillation regimes, both of which significantly differ from that of bubble near a rigid boundary. In the two regimes, the micro-jets are triggered by the collision of a fluid inflow at the symmetry axis of the bubble. We provide time-resolved evidence that these micro-jets are initially atomized before stabilizing into fully liquid micro-jets that move through the bubble. The atomized part of the micro-jets can reach velocities of up to 2000 m/s, while the liquid part can reach velocities of up to 1000 m/s. Finally, we propose a procedure using the Virtual Frame Technique to track the extremely fast dynamics of cavitation bubbles with a single shadowgraph captured on a consumer-level camera. Altogether, the results presented in this thesis provide a better understanding of the effects of deformable boundaries on the bubble's behavior and yield insights into the mechanisms leading to extremely fast and potentially damaging micro-jets.