Evidence for exocomets, icy bodies in extrasolar planetary systems, has rapidly increased over the past decade. Volatiles are detected through the gas that exocomets release as they collide and grind down within their natal belts, or as they sublimate once scattered inwards to the regions closest to their host star. Most detections are in young, 10 to a few 100 Myr-old systems that are undergoing the final stages of terrestrial planet formation. This opens the exciting possibility to study exocomets at the epoch of volatile delivery to the inner regions of planetary systems. Detection of molecular and atomic gas in exocometary belts allows us to estimate molecular ice abundances and overall elemental abundances, enabling comparison with the Solar Nebula and Solar System comets. At the same time, observing star-grazing exocomets transiting in front of their star (for planetary systems viewed edge-on) and exozodiacal dust in the systems’ innermost regions gives unique dynamical insights into the inward scattering process producing delivery to inner rocky planets. The rapid advances of this budding subfield of exoplanetary science will continue in the short term with the upcoming JWST, WFIRST and PLATO missions. In the longer term, the priority should be to explore the full composition of exocomets, including species crucial for delivery and later prebiotic synthesis. Doing so around an increasingly large population of exoplanetary systems is equally important, to enable comparative studies of young exocomets at the epoch of volatile delivery. We identify the proposed LUVOIR and Origins flagship missions as the most promising for a large-scale exploration of exocometary gas, a crucial component of the chemical heritage of young exo-Earths. ar X iv :1 90 4. 02 71 5v 1 [ as tr oph .E P] 4 A pr 2 01 9 1 Background and Motivation Understanding the origin of life stands as one of the main drivers of interdisciplinary research that includes chemistry, biology and geology as well as astronomy. The development of prebiotic molecules requires not only particular physical conditions, but also the presence of simple feedstock volatile molecules like water, cyanides and sulfides (e.g. Patel et al., 2015). Young and dry rocky planets may be lacking in these volatiles (Albarède, 2009), requiring external delivery from volatile-rich comets. By comet, we refer to the IAU definition of a body made of rock and ice, typically a few kilometres in diameter, and consider all minor bodies that contain a significant amount of ice, be they in stable orbits within their outer reservoirs, or be they scattered inwards and evaporating as they approach the central star. Young comets, in the Solar Nebula and its extrasolar counterparts, form from the coagulation of dust and freeze-out of major gas species onto their surface. In the first ∼10 Myr of this gas-rich environment, comets may accrete to form icy worlds as seen in the outer reaches of the Solar System, or end up in stable long-period orbits, forming rings and broader belts. These belts, such as our own Edgeworth-Kuiper belt, are broadly termed planetesimal belts or debris disks. These belts of exocomets survive the dissipation of protoplanetary disks and are later observed throughout the lifetime of the stars. Exocometary belts significantly more massive than today’s Kuiper belt are present around at least∼20% of nearby stars, producing observable dust and losing mass over time through collisional grinding (see White Paper by Gaspar et al.). The most massive and easily detectable belts are therefore the youngest, at ages of 10 to 100 Myr. Crucially, this is the point at which planetary systems undergo the violent era of planetary assembly, when the dynamical action of recently formed planets on exocomets is most likely to produce inward scattering (e.g. Morbidelli et al., 2012) and volatile delivery to the inner, rocky young Earth analogs. Assessing the potential for volatile delivery in planetary systems is the key driver for research investigating the dynamics and composition of exocomets. Studies of solids within belts of exocomets have been successfully conducted for the past three decades (see White Papers by Gaspar et al., Su et al.). Here, we highlight the exocometary aspect, i.e. studies of the volatile composition and inward scattering of exocomets, which are most relevant to the issue of volatile delivery. These studies have seen significant advances in the past decade, giving rise to the field of Exocometary Science. In this White Paper, we summarize these advances and outline the observational requirements for the field to continue to prosper in the next decade and beyond. Figure 1: Left: Ca II K line profile of β Pictoris, showing a stable absorption feature from exocometary gas in the outer belt, as well as time-variable, high-velocity components from star-grazing exocomets on eccentric orbits. Adapted from Kiefer et al. (2014). Right: Elemental abundances of exocometary gas in the outer disk of β Pic, from studies of the stable absorption component. Adapted from Roberge et al. (2006), with the addition of the oxygen abundance estimate of Brandeker et al. (2016), and the hydrogen and nitrogen abundance from Wilson et al. (2017, 2019).