The era of exoplanet characterization is upon us. For a subset of exoplanets -the transiting planets -physical properties can be measured, including mass, radius, and atmosphere characteristics. Indeed, measuring the atmospheres of a further subset of transiting planets, the hot Jupiters, is now routine with the Spitzer Space Telescope. The James Webb Space Telescope (JWST) will continue Spitzer's legacy with its large mirror size and precise thermal stability. JWST is poised for the significant achievement of identifying habitable planets around bright M through G stars-rocky planets lacking extensive gas envelopes, with water vapor and signs of chemical disequilibrium in their atmospheres. Favorable transiting planet systems, are, however, anticipated to be rare and their atmosphere observations will require tens to hundreds of hours of JWST time per planet. We review what is known about the physical characteristics of transiting planets, summarize lessons learned from Spitzer high-contrast exoplanet measurements, and give several examples of potential JWST observations.