Transmission spectroscopy has been a valuable tool in characterizing the atmospheres of extrasolar planets. This method requires obtaining a spectrum while a transiting exoplanet passes in front of its host star. The starlight that filters through the upper atmosphere of the planet leaves a spectral fingerprint that can be indicative of the planet’s atmospheric composition, the presence of clouds or hazes, and atmospheric circulation or winds. I will talk about theoretical modeling and observational results centering on transmission spectroscopy of two particularly interesting classes of exoplanets – super-Earths (or planets with masses between 1 and 10 times that of the Earth) and hot Jupiters (highly irradiated giant planets with very short orbital periods). Super-Earths and hot Jupiters are not present in our own solar system, and they therefore represent fundamentally new types of planets to study. Many surprises have resulted from both the theoretical and observational work at this cosmic frontier. I will focus specifically on the first characterization of a super-Earth atmosphere (of the planet GJ 1214b) and on the possibility of using transmission spectroscopy to constrain atmospheric circulation in the atmospheres of hot Jupiters.