This review describes the saga of the atom and molecules, from the atomic concept as it was introduced 25 centuries ago by Leucippus and Democritus, to the modern Quantum Molecular Modeling. Quantum methods that have given rise to the contemporary Molecular Modeling are briefly presented. Chosen examples illustrate the performance and the predictions of Quantum Modeling in the following topics: conformational analysis, electrostatics, molecular spins and radicals, infrared and Raman spectra, thermochemistry, and electrophilicity properties derived from the molecular chemical potential.