Hill climbing is a local search algorithm that evaluates the current state and moves to a neighboring state that improves the value of the objective function. It continues moving to better states until a local optimum is reached. Problems with hill climbing include getting stuck at local optima rather than the global optimum, flat areas where no improving moves are possible, and ridges where it is limited to moving in one direction. Applications of hill climbing include network flow problems, the traveling salesman problem, and integrated circuit design.