When musicians compose the harmony, they usually try various possible combinations of the music pitches stored in their memory, which can be considered as a optimization process of adjusting the input (pitches) to obtain the optimal output (perfect harmony). Harmony search draws the inspiration from harmony improvisation, and has gained considerable results in the field of optimization, although it is a relatively NIC algorithm. With mimicking the rules of various combining pitches, harmony search has two distinguishing operators different from other NIC algorithms: harmony memory considering rate (HMCR) and pitch adjusting rate (PAR) that are used to generate and further mutate a solution, respectively. This candidate generation mechanism and single search memory involved decide its excellence in structure simplicity and small initial population. This chapter presents the discussions of the inspiration of harmony search, the basic harmony search optimization algorithm, and an overview of different application areas of the harmony search.