PetroHead is a numerical dynamic partial equilibrium model for the world oil, gas and coal markets. Its main outputs are figures for yearly regional consumption, production, prices and emissions associated with oil, gas and coal for the time period from 2013 to 2100. The model also includes biofuels, which we model as a perfect substitute for oil. Both production and consumption feature dynamic elements. The oil and gas producers maximize the present value of their resource, implying that oil and gas prices contain scarcity rents. In addition, the supply side features sluggish production capacity. This is implemented such that current production capacity increases based on past production levels. The demand side also features sluggishness in the sense of habit formation. That is, present demand for one type of fuel depends positively on past consumption of that fuel. This allows the model to differentiate between short- and long-run elasticities.