The van der Waals' bonding of atoms and molecules has become an increasingly important topic of study in the past few years in many areas of physical chemistry. One of the challenges of such studies is to characterize where weak, "physical" (multipole) interactions are sufficient to describe the bonding, and where stronger "chemical" (electron-sharing) interactions begin to be important. We show in this Feature Article that the bonding in complexes of ground-state Hg(6s6s1S0) and excited-state Hg(6s6p3P1) with rare-gas atoms and small molecules varies from purely physical to strongly chemical. In complexes of the filled-shell Hg(6s6s1S0) state with rare gases and molecules such as H-2, CH4, NH3, or H2O the bonding and structure can be understood within the context of weak, long-range multipolar interactions and short-range Pauli repulsions: "physical" (van der Waals) bonding. On the other hand, such interactions in the analogous complexes of the excited Hg(6s6p3P1) state can vary from essentially physical (with rare gases or CH4) to chemical (with H2O, NH3, H-2, or Hg).