Smart materials are intelligent materials that change their structural, chemical, mechanical, or thermal properties in response to an external stimulus such as heat, light, and magnetic and electric fields. With the increase in usage of smart materials in many sensitive applications, the need for a remote, wireless, efficient, and biologically safe stimulus has become crucial. This dissertation addresses this requirement by using high intensity focused ultrasound (HIFU) as the external trigger. HIFU has a unique capability of maintaining both spatial and temporal control and propagating over long distances with reduced losses, to achieve the desired response of the smart material. Two categories of smart materials are investigated in this research; shape memory polymers (SMPs) and piezoelectric materials. SMPs have the ability to store a temporary shape and returning to their permanent or original shape when subjected to an external trigger. On the other hand, piezoelectric materials have the ability to convert mechanical energy to electrical energy and vice versa. Due to these extraordinary properties, these materials are being used in several industries including biomedical, robotic, noise-control, and aerospace. This work introduces two novel concepts: First, HIFU actuation of SMP-based drug delivery capsules as an alternative way of achieving controlled drug delivery. This concept exploits the pre-determined shape changing capabilities of SMPs under localized HIFU exposure to achieve the desired drug delivery rate. Second, solving the existing challenge of low efficiency by focusing the acoustic energy on piezoelectric receivers to transfer power wirelessly. The fundamental physics underlying these two concepts is explored by developing comprehensive mathematical models that provide an in-depth analysis of individual parameters affecting the HIFU-smart material systems, for the first time in literature. Many physical factors such as acoustic, material and dynamical nonlinearities, acoustic standing waves, and mechanical behavior of materials are explored to increase the developed models' accuracy. These mathematical frameworks are designed with the aim of serving as a basic groundwork for building more complex smart material-based systems under HIFU exposure. / Doctor of Philosophy / Smart materials are a type of intelligent materials that have the ability to respond to external stimuli such as heat, light, and magnetic fields. When these materials respond, they can change their structural, thermodynamical, mechanical or chemical nature. Due to this extraordinary property, smart materials are being used in many applications including biomedical, robotic, space, microelectronics, and automobile industry. However, due to increased sensitivity and need for safety in many applications, a biologically safe, wireless, and efficient trigger is required to actuate these materials. In this dissertation, sound is used as an external trigger to actuate two types of smart materials: shape memory polymers (SMPs) and piezoelectric materials. SMPs have an ability to store a temporary (arbitrarily deformed) shape and return to their permanent shape when exposed to a trigger. In this dissertation, focused sound induced thermal energy acts as a trigger for these polymers. A novel concept of focused ultrasound actuation of SMP-based drug delivery capsules is proposed as a means to solve some of the challenges being faced in the field of controlled drug delivery. Piezoelectric materials have an ability to generate electric power when an external mechanical force is applied and vice versa. In this study, sound pressure waves supply the external force required to produce electric current in piezoelectric disks, as a method for achieving power transfer wirelessly. This study aims to solve the current problem of low efficiency in acoustic power transfer systems by focusing sound waves. This dissertation addresses the fundamental physics of high intensity focused ultrasound actuation of smart materials by developing comprehensive mathematical models and systematic experimental investigations, that have not been performed till now. The developed models enable an in-depth analysis of individual parameters including nonlinear material behavior, acoustic nonlinearity and resonance phenomena that affect the functioning of these smart systems. These mathematical frameworks also serve as groundwork for developing more complex systems.