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Mercury probably formed hot with early differentiation of an iron core. If this core is pure iron, then it would have frozen very quickly. However, volatile-bearing planetesimals most likely contributed to the accretion of the planet Mercury, adding a small amount of sulfur. Under these conditions, the strongly depressed Fe-S eutectic has prevented the Mercurian core from freezing completely. Detailed models incorporating subsolidus convection of the Mercurian mantle indicate that, to date, it may be possible to maintain convection in the outer fluid core of Mercury, perhaps allowing for dynamo generation of the observed magnetic field. A total sulfur abundance of around 2 to 3% by mass relative to iron allows for both the rapid growth of an inner core prior to cessation of early bombardment (to satisfy the geological constraint of little planetary contraction over geologic time), and the possibility of ongoing outer core convection. The role of tidal heating in the inner solid core is also assessed and found to be a potentially significant contribution to the core energy budget in favorable circumstances, enhancing or prolonging outer core thermal convection. Permanent magnetism is at best a marginal explanation of the magnetic field. A fluid outer core is a desirable feature of the present structure. However, it is not certain whether the criteria for dynamo generation are currently satisfied; estimates of the field expected for a dynamo are one to two orders of magnitude in excess of the observed field. Alternative explanations. including the possibility of a weak thermoelectric dynamo, are discussed.