  We have recently hit the milestone of 5,000 exoplanets discovered. In stark
contrast with the Solar System, most of the exoplanets we know to date orbit
extremely close to their host stars, causing them to lose copious amounts of
gas through atmospheric escape at some stage in their lives. In some planets,
this process can be so dramatic that they shrink in timescales of a few million
to billions of years, imprinting features in the demographics of transiting
exoplanets. Depending on the transit geometry, ionizing conditions, and
atmospheric properties, a planetary outflow can be observed using transmission
spectroscopy in the ultraviolet, optical or near-infrared. In this review, we
will discuss the main techniques to observe evaporating exoplanets and their
results. To date, we have evidence that at least 28 exoplanets are currently
losing their atmospheres, and the literature has reported at least 42
non-detections.
