One of the simplest questions that can be asked about molecular diversity is how many organic molecules are possible in total? To answer this question, my research group has computationally enumerated all possible organic molecules up to a certain size to gain an unbiased insight into the entire chemical space. Our latest database, GDB-17, contains 166.4 billion molecules of up to 17 atoms of C, N, O, S, and halogens, by far the largest small molecule database reported to date. Molecules allowed by valency rules but unstable or nonsynthesizable due to strained topologies or reactive functional groups were not considered, which reduced the enumeration by at least 10 orders of magnitude and was essential to arrive at a manageable database size. Despite these restrictions, GDB-17 is highly relevant with respect to known molecules. Beyond enumeration, understanding and exploiting GDBs (generated databases) led us to develop methods for virtual screening and visualization of very large databases in the form of a "periodic system of molecules" comprising six different fingerprint spaces, with web-browsers for nearest neighbor searches, and the MQN- and SMIfp-Mapplet application for exploring color-coded principal component maps of GDB and other large databases. Proof-of-concept applications of GDB for drug discovery were realized by combining virtual screening with chemical synthesis and activity testing for neurotransmitter receptor and transporter ligands. One surprising lesson from using GDB for drug analog searches is the incredible depth of chemical space, that is, the fact that millions of very close analogs of any molecule can be readily identified by nearest-neighbor searches in the MQN-space of the various GDBs. The chemical space project has opened an unprecedented door on chemical diversity. Ongoing and yet unmet challenges concern enumerating molecules beyond 17 atoms and synthesizing GDB molecules with innovative scaffolds and pharmacophores.