Inverse problems form a multidisciplinary area involving mathematics, sciences, engineering, and various other fields, where the basic aim is to determine a cause from its known effects. Expertise in this area requires a good understanding of the corresponding direct problem, for which the goal is to determine the effects from its given cause. In this public lecture to a high school audience, inverse problems are described and various applications are indicated. Some such applications include designing of photonic crystals (i.e., nanostructures which can be used in computer circuitry where the information is carried by a flow of light rather than by an electrical current), using remote sensing for oil exploration, and determining forces among elementary particles by understanding how such particles scatter from each other. NOTE: The length of the talk can be adjusted to last from 40 to 60 minutes. The goal is to encourage students to study mathematics, sciences, and engineering in college and to choose careers in these fields. Presenter will need and LCD projector, cable connect for a laptop computer, a screen or other suitable projection surface, and an Internet connection.