Synthesis of molecules in a combinatorial fashion can quickly lead to large numbers of molecules.  For example, a molecule with three points of diversity (R, R, and R) can generate  possible structures, where , , and  are the numbers of different substituents utilized.
The basic principle of combinatorial chemistry is to prepare libraries of a very large number of compounds then identify the useful components of the libraries.
Although combinatorial chemistry has only really been taken up by industry since the 1990s, its roots can be seen as far back as the 1960s when a researcher at Rockefeller University, Bruce Merrifield, started investigating the solid-phase synthesis of peptides.
In its modern form, combinatorial chemistry has probably had its biggest impact in the pharmaceutical industry. Researchers attempting to optimize the activity profile of a compound create a library of many different but related compounds. Advances in robotics have led to an industrial approach to combinatorial synthesis, enabling companies to routinely produce over 100,000 new and unique compounds per year.
In order to handle the vast number of structural possibilities, researchers often create a virtual library, a computational enumeration of all possible structures of a given pharmacophore with all available reactants.  Such a library can consist of thousands to millions of virtual compounds.  The researcher will select a subset of the virtual library for actual synthesis, based upon various calculations and criteria (see ADME, computational chemistry, and QSAR).