The planet Mercury, a difficult object for study by astronomical observation and spacecraft exploration alike, poses multiple challenges to our general understanding of the inner planets. Mercury's anomalously high uncompressed density implies a metal fraction of 60% or more by mass, an extreme outcome of planetary formational processes common to the inner solar system. Whether that outcome was the result of chemical gradients in the early solar nebula or removal by impact or vaporization of most of the silicate shell from a differentiated protoplanet can potentially be distinguished on the basis of the chemical composition of the present crust. Our understanding of the geological evolution of Mercury and how it fits within the known histories of the other terrestrial planets is restricted by the limited coverage and resolution of imaging by the only spacecraft to have visited the planet. The role of volcanism in Mercury's geological history remains uncertain, and the dominant tectonic structures are lobate scarps interpreted as recording an extended episode of planetary contraction, issues that require global imaging to be fully examined. That Mercury has retained a global magnetic field when larger terrestrial planets have not stretches the limits of standard hydromagnetic dynamo theory and has led to proposals for a fossil field or for exotic dynamo scenarios. Hypotheses for field generation can be distinguished on the basis of the geometry of Mercury's internal field, and the existence and size of a fluid outer core on Mercury can be ascertained from measurements of the planet's spin axis orientation and gravity field and the amplitude of Mercury's forced librations. The nature of Mercury's polar deposits, suggested to consist of volatile material cold-trapped on the permanently shadowed floors of high-latitude impact craters, can be tested by remote sensing of the composition of Mercury's surface and polar atmosphere. The extremely dynamic exosphere, which includes a number of species derived from Mercury's surface, offers a novel laboratory for exploring the nature of the complex and changing interactions among the solar wind, a small magnetosphere, and a solid planet. Recent ground-based astronomical measurements and several new theoretical developments set the stage for the in-depth exploration of Mercury by two spacecraft missions within the coming decade.