When extrasolar planets are observed to transit their parent stars, we are granted unprecedented access to their physical properties. It is only for transiting planets that we are permitted direct estimates of the planetary masses and radii, which provide the fundamental constraints on models of their physical structure. In particular, precise determination of the radius may indicate the presence (or absence) of a core of solid material, which in turn would speak to the canonical formation model of gas accretion onto a core of ice and rock embedded in a protoplanetary disk. Furthermore, the radii of planets in close proximity to their stars are affected by tidal effects and the intense stellar radiation. As a result, some of these "hot Jupiters" are significantly larger than Jupiter in radius. Precision follow-up studies of such objects (notably with the spacebased platforms of the Hubble and Spitzer Space Telescopes) have enabled direct observation of their transmission spectra and emitted radiation. These data provide the first observational constraints on atmospheric models of these extrasolar gas giants, and permit a direct comparison with the gas giants of the solar system. Despite significant observational challenges, numerous transit surveys and quick-look radial velocity surveys are active, and promise to deliver an ever-increasing number of these precious objects. The detection of transits of short-period Neptune-sized objects, whose existence was recently uncovered by the radialvelocity surveys, is eagerly anticipated. Ultraprecise photometry enabled by upcoming space missions offers the prospect of the first detection of an extrasolar Earth-like planet in the habitable zone of its parent star, just in time for Protostars and Planets VI.