Ultrasound contrast agents are comprised of microscopic-sized bubbles – encapsulated with a shell of surfactant, polymer or protein – that are injected intravenously to enhance blood-tissue contrast in ultrasound imaging. More recently, encapsulated microbubbles (EMBs) are emerging as powerful tools for noninvasive therapeutic treatments ranging from drug delivery to tumor destruction. To utilize EMBs effectively in biomedical applications, it is necessary to understand the effect of the incident ultrasound on the radial and shape dynamics of microbubbles. For example, the nonlinear radial response of EMBs is essential for ultrasound imaging, while nonspherical shape instabilities can be an important mechanism for enhancing drug uptake or tissue ablation. In this talk, various models of EMBs will be discussed and the results of numerical simulations presented. It will be shown that the shell and ultrasound properties strongly influence the EMB dynamics. This leads to the prospect of optimizing the shell properties and ultrasound protocols to control the EMB response based on its specific application.