  Rocky planets are common around other stars, but their atmospheric properties
remain largely unconstrained. Thanks to a wealth of recent planet discoveries
and upcoming advances in observing capability, we are poised to characterize
the atmospheres of dozens of rocky exoplanets in this decade. Theoretical
understanding of rocky exoplanet atmospheres has advanced considerably in the
last few years, yielding testable predictions of their evolution, chemistry,
dynamics and even possible biosignatures. Here we review key progress in this
field to date and discuss future objectives. Our major conclusions are as
follows:
  1) Many rocky planets may form with initial H$_2$-He envelopes that are later
lost to space, likely due to a combination of stellar UV/X-ray irradiation and
internal heating.
  2) After the early stages of evolution, a wide diversity of atmospheric
compositions is expected, due to variations in host star flux, atmospheric
escape rates, interior exchange and other factors.
  3) Observations have ruled out the presence of hydrogen-dominated atmospheres
on several nearby rocky exoplanets, and the presence of any thick atmosphere on
one target. More detailed atmospheric characterization of these planets and
others will become possible in the near future.
  4) Exoplanet biosphere searches are an exciting future goal. However,
reliable detections for a representative sample of planets will require further
advances in observing capability and improvements in our understanding of
abiotic planetary processes.
