Search is a fundamental problem among many communities including robotics. Some examples of search applications are search-and-rescue, environmental monitoring with the purpose of controlling the population of invasive species or preserving endangered animals, and warfare strategy design. Formally, in a search problem the task is to find a mobile target that is either adversarial or stochastic. The adversarial target is actively avoiding capture, while the stochastic target is not aware of the searcher and is moving independently. In addition to the target’s motion model, the environment complexity and searcher’s limited sensing capabilities make the problem more challenging. In the first part of this talk, I present our pursuit-evasion results that concern the problem of capturing an adversarial target. We will see how a pursuer with complete sensing can capture the evader on geodesic terrains. We also discuss winning strategies for the pursuer when it has limited information about the location of an adversarial evader. In the second part of this talk, I will present search strategies for finding a random walker which moves on a line or in a grid environment. The strategies are designed such that the capture probability subject to energy and time constraints is maximized.