The discoveries of extrasolar planets by Wolszczan, Mayor and Queloz, Butler et al., and others have stimulated a widespread effort to obtain a body of data sufficient to understand their occurrence and characteristics. Doppler velocity techniques have found dozens of extrasolar planets with masses similar to that of Jupiter. Approximately ten percent of the stars that show planets with orbital periods of a few days to a week are expected to show transits. With the mass obtained from Doppler velocity measurements and the size from transit photometry, the densities of the planets can be determined. Theoretical models of the structure of "hot Jupiters" (i.e., those planets within a tenth of an astronomical unit (AU) of the parent star) indicate that these planets should be substantially larger in size and lower in density than Jupiter. Thus the combination of transit and Doppler velocity measurements provide a critical test of the theories of planetary structure. Furthermore, because photometry can be done with small-aperture telescopes rather than requiring the use of much larger telescopes, transit photometry should also reduce the cost of discovering extrasolar planets.