This sequence of lectures will focus on online strategies for exploration and search in combinatorial environments. We introduce the concept of competitive analysis with some simple examples, including list updates in linear sequences. Competitive analysis has become the main tool for analyzing the worst case behaviour of online strategies for exploration and search. We exhibit some results on online search and exploration including searching for a target point on a line with a single agent, searching for a target on multiple lines with several agents, geometric exploration of simple polygons with a single agent and some results on exploration of trees with multiple agents.