For many years the assumption that "Chemical compounds with similar structures may have similar activities" has been a foundation for lead identification. The similarity can be computed based upon topological, steric, electronic, and/or physical properties. The chemical structure similarity search differs from the chemical substructure search in that the former requires assessment of the properties of each compound and thus no filter can be applied for skipping structures before they are assessed to accelerate the computation. The latter can be accelerated by pre-screening compounds and omitting those that miss one (or more) specified fragments from the query. Moreover, three-dimensional similarity search requires superimposing many conformation pairs for each compound in the library. This makes 3-D similarity search algorithms time-consuming, and in general requires high performance computing (HPC) resources. This review will summarize recent progress in the techniques for HPC-supported two and three-dimensional chemical structure similarity search algorithms, and their applications in ligand-based virtual screening.