The atmospheres of planets orbiting other stars may be studied by the technique of transit spectroscopy. This technique needs a very high SNR, so large space telescopes are needed, and bright target stars must be found. This paper uses planetary atmosphere models to discuss the SNR performance required to achieve specific science goals for both giant Jupiter-like planets and for small Earth-like planets. It discusses the space telescopes to survey bright stars to find suitable target stars, and the designs of large space telescopes to perform the transit spectroscopy.