The linear and non-linear oscillations of microbubbles excited by ultrasound, known as acoustic cavitation, have a broad range of therapeutic applications ranging from minimally invasive surgery to drug delivery. There are however several interesting challenges remaining in order to facilitate and optimize the clinical adoption of ultrasound-mediated therapies. Firstly, application-specific cavitation nuclei need to be developed, which exhibit an appropriate acoustic response, remain stable in the bloodstream and are suitably sized to penetrate biological targets: several novel approaches, involving nanobubbles stabilized on a solid nanoparticle surface, superheated droplets, or magnetically responsive microbubbles, will be presented. Secondly, in the context of drug delivery, cavitational microstreaming needs to be better understood as a mechanism that mediates the active transport and mixing of nanomedicines in the vicinity of the bubble: the effect of the physical properties of both the cavitation nucleation agent and the nanomedicine will be explored. Finally, to ensure both treatment safety and efficacy, the relationship between bubble dynamics and tissue damage needs to be better understood as a function of both cellular biomechanics and the bulk viscoelastic properties of tissue. Illustrative examples involving both theoretical modelling and experimental results across the areas of sonoporation, oncological drug delivery, sonothrombolysis and histotripsy for orthopaedic applications will be presented.