The ignition of plasma in underwater gas bubbles is a promising method of injecting chemically reactive species into liquids for applications in environmental remediation. To date, these studies have been limited to bubbles attached to the surface of the electrode. This dissertation proposes that plasma can be ignited in bubbles that are separated from the electrode by first deforming the shape of the bubble;;s dielectric boundary. This approach exploits a phenomenon termed the shape effect, in which the distortion of the dielectric boundary distorts and enhances the applied electric field in the volume of the bubble. The purpose of this dissertation was two-fold: (1) to demonstrate the shape effect by exciting strong deformations in underwater bubbles, and (2) investigate the fundamental mechanisms responsible for plasma formation in isolated bubbles. To accomplish this goal, an experimental apparatus was developed, capable of confining the bubble, deforming the shape of the bubble, and igniting plasma within the bubble interior. The apparatus utilizes ultrasonic acoustic standing waves to trap the bubble at a fixed position underwater and apply electric fields using electrodes that are mounted on a 3D translation stage.In general, it was observed that electric fields in the range 10-25 kV/cm were capable of exciting bubbles into a wide variety of nonlinear deformations, including resonant capillary waves on the bubble surface, spherical harmonic perturbations, and in some cases the complete breakup of the bubble into multiple fragments. Simulations of the electric field in these deformed bubbles indicate that the enhancement of the applied field could be as large as a factor of 10-50. A thorough investigation of fundamental discharge mechanisms in bubble filled liquids was also undertaken. It was shown that in a specific range of voltage and electrode geometry, a new type of streamer is observed that travels through the both liquid and the bubble gas. Under careful adjustment of the operating conditions, the plasma could actually be confined to the bubble when driven by a 12 kV pulse. It was further observed that this isolated bubble plasma could be ignited much easier using a repetitively pulsed voltage source.