The majority of volatile organic compounds emitted from the terrestrial biosphere (BVOCs) are highly reactive hydrocarbons that have been shown to affect atmospheric composition across the full range of temporal scales from fractions of seconds to centuries and spatial scales from μm to global. Furthermore, biogenic emissions are thought to account for around 90 % of the total quantity of non-methane hydrocarbons released into the atmosphere each year. As a result, BVOCs have substantial air quality and climate impacts, and there is an urgent need to quantify and map their emissions as precisely as possible. In this chapter we outline the use of computer models to estimate annual global emissions of BVOCs and the on-going efforts to validate and constrain the output from such models. The current generation of BVOC emission models generally includes only the constitutive emissions of a handful of compounds: chiefly isoprene, monoterpenes and methanol, which are thought to account for about 80 % of the total flux from the biosphere. At present, it is estimated by global models that total annual emission of isoprene amounts to around 500 Tg of carbon, with the emissions dominated by tropical ecosystems and by tree species. The emissions of monoterpenes are similarly distributed, although high levels of monoterpene emissions are also seen from the boreal forests. There is currently no consensus on the annual estimate of monoterpene emission, with estimates ranging from 30 to 150 Tg of carbon. Apart from these main compounds, the biosphere emits many hundreds of different compounds, some of which are produced as a short-lived, transient response to stress rather than as constitutive emissions. We discuss the role that biogenic emissions of reactive trace gases play in the Earth system as a whole, and consider the potential feedbacks that exist between BVOC emissions, atmospheric composition, air quality and climate, and the terrestrial biosphere, and how these can be studied with Earth system models. We finally suggest ways of improving and further developing the global models.