Researchers who are active and often pioneers in the field explain how to provide mathematically non-sophisticated molecular descriptions encompassing three-dimensional aspects of molecules, which allow an easy intuitive grasp of their significance, the possibility of computing them for any imaginable structure, and their use in molecular modeling for drug design. Among the topics are descriptors of molecular shape in three dimensions, recognizing membrane protein structure from an amino acid sequence, recent work on toriodal and other exotic Fullerene structures, and the application of topology and graph theory in understanding inorganic molecules. For graduate and research chemists and mathematicians.