Over the past decade, rapidly increasing evidence for exocomets, icy bodies in extrasolar planetary systems, has given rise to the budding field of Exocometary Science.  Exocomets are detected through the gas and dust they release as they collide and grind down within their natal belts, or – like Solar System comets – as they sublimate once moving inwards to the regions closest to their host star. The majority of detections are in relatively young, 10-100 Myr-old planetary systems, where terrestrial exoplanets are undergoing the final stages of formation.  This opens the exciting possibility to study exocomets at the epoch where delivery of volatiles (including water) to forming terrestrial planets is most likely.   In this talk, I will present a broad overview of the different lines of evidence for exocomets from UV to mm wavelengths.  In particular, I will show how detection of molecular and atomic gas allows us to estimate molecular ice abundances and elemental abundances in young exocomets, enabling comparison with the Solar Nebula and Solar System comets.  Finally, I will link exocomet compositions to their origins in protoplanetary disks, discussing evidence for a preferential belt formation location which is dependent on the host star’s luminosity.