The numerical encoding of chemical structure with Topological Indices (TIs) is currently growing in importance in Medicinal Chemistry and Bioinformatics. This approach allows the rapid collection, annotation, retrieval, comparison and mining of chemical structures within large databases. TIs can subsequently be used to seek quantitative structure-activity relationships (QSAR), which are models connecting chemical structure with biological activity. In the early 1990s, there was an explosion in the introduction and definition of new TIs. The Handbook of Molecular Descriptors by Todeschini and Consonni lists more than 1500 of these indices. At the end of the last century, researchers produced a large number of TIs with essentially the same advantages and/or disadvantages. Consequently, many researchers abandoned the definition of TIs for a time. In our opinion, one of the problems associated with TIs is that researchers aimed their efforts only at the codification of chemical connectivity for small-sized drugs. As a consequence, recently it seems that we have arrived at “Fukuyamas End of History in TIs definition”. In the work described here, we review and comment on the “quo vadis” and challenges in the definition of TIs as we enter the new century. Emphasis is placed on new chiral TIs (CTIs), flexible TIs for unifying QSAR models with multiple targets, topographic indices (TPGIs), TIs for DNA and protein sequences, TIs for 2D RNA structures, TPGIs and drug-protein or drug-RNA quantitative structure-binding relationship (QSBR) studies, TIs to encode protein surface information and TIs for protein interaction networks (PINs).