The study of bubble dynamics in non-uniform flow fields is fundamental to the ability to predict or explain any cavitation effects in real flow fields. In this presentation we describe our recent contributions towards the fundamental understanding of bubble dynamics in non-uniform flow fields when large bubble deformations and bubble interactions are taken into account. A 3D Boundary Element Method is developed to describe the non-spherical bubble dynamics of each bubble in the flow, incorporating the influence of the underlying flow field which can be viscous. The method is used to study bubble dynamics in relatively simple fundamental flow fields such as the dynamics of bubbles in a shear flow near a flat wall, or in the flow field of a vortex line. It is then shown that bubble splitting, shearing off and development of surface instabilities are probably as common as the classical reentering jet formation.