Extrasolar planets can be detected photometrically by their transits across the parent star, in a small percentage of systems fortuitously oriented with respect to the line of sight. This paper develops statistical models to connect observed transit statistics to the underlying planetary system characteristics. Monte Carlo simulations of the solar system provide a guide for transit surveys of solar-type stars: about 1.2% of all systems will show an individually detectable transit, usually within 1 year; 0.07--0.14% will show transits of two or more planets; 7--10% of all systems showing a large terrestrial planet transit will subsequently show a gas giant transit. Transit statistics for a large numbers of planetary systems can reveal characteristics important to formation: statistical distributions of orbital semimajor axes and planetary sizes, mean relative orbital inclination, and mean number of planets per system. Orbital eccentricities of the order of those characterizing the solar system will have little discernible effect on transit statistics. ¿ American Geophysical Union 1996