Future high-precision photometric measurements of transiting extrasolar planets promise to tell us much about the characteristics of these systems. We examine how atmospheric lensing and (projected) planet oblateness/ellipticity modify transit light curves. The large density gradients expected in planet atmospheres can offset the unfavorably large observer lens–to–source lens distance ratio and allow the existence of caustics. Under such conditions of strong lensing, which we quantify with an analytic expression, starlight from all points in the planet's shadow is refracted into view, producing a characteristic slowing down of the dim- ming at ingress (vice versa for egress). A search over several parameters, such as the limb-darkening profile, the planet radius, the transit speed, and the transit geometry, cannot produce a nonlensed transit light curve that can mimic a lensed light curve. The fractional change in the diminution of starlight is approximately the ratio of atmospheric scale height to planet radius, expected to be 1% or less. The lensing signal varies strongly with wavelength－caustics are hidden at wave bands where absorption and scattering are strong. Planet oblateness induces an asymmetry to the transit light curve about the point of minimum flux, which varies with the planet orientation with respect to the direction of motion. The fractional asymmetry is at the level of 0.5% for a projected oblateness of 10%, independent of whether or not lensing is important. For favorable ratios of planet radius to stellar radius (i.e., gas giant planets), the above effects are potentially observable with future space-based missions. Such measurements could constrain the planet shape and its atmospheric scale height, density, and refractive coefficient, providing information on its rotation, temperature, and composition. We have examined a large range of planetary system parameter space including the planetary scale height and orbital distance. For HD 209458b, the only currently known transiting extrasolar planet, caustics are absent because of the very small lens-source separation (and a large scale height caused by a high temperature from the small separation). Its oblateness is also expected to be small because of the tidal locking of its rotation to orbital motion. Finally, we provide estimates of other variations to transit light curves that could be of comparable importance—including rings, satellites, stellar oscillations, star spots, and weather.