Our understanding of the physical and chemical structure of pre-stellar cores, the simplest star-forming sites, has significantly improved since the last IAU Symposium on Astrochemistry (South Korea, 1999). Research done over these years has revealed that major molecular species like CO and CS systematically deplete onto dust grains in the interior of pre-stellar cores, while species like N2H+ and NH3 survive in the gas phase and can usually be detected toward the core centers. Such a selective behavior of molecular species gives rise to a differentiated (onion-like) chemical composition, and manifests itself in molecular maps as a dichotomy between centrally peaked and ring-shaped distributions. From the point of view of star-formation studies, the identification of molecular inhomogeneities in cores helps to resolve past discrepancies between observations made using different tracers, and brings the possibility of self-consistent modelling of the core internal structure. Here I present recent work on determining the physical and chemical structure of two pre-stellar cores, L1498 and L1517B, using observations in a large number of molecules and Monte Carlo radiative transfer analysis. These two cores are typical examples of the pre-stellar core population, and their chemical composition is characterized by the presence of large ‘freeze out holes’ in most molecular species. In contrast with these chemically processed objects, a new population of chemically young cores has begun to emerge. The characteristics of its most extreme representative, L1521E, are briefly reviewed.