We analyze the dynamics of global fossil resource markets under different assumptions for the supply of fossil fuel resources, development pathways for energy demand, and climate policy settings. Resource markets, in particular the oil market, are characterized by a large discrepancy between costs of resource extraction and commodity prices on international markets. We explain this observation in terms of (a) the intertemporal scarcity rent, (b) regional price differentials arising from trade and transport costs, (c) heterogeneity and inertia in the extraction sector. These effects are captured by the REMIND model. We use the model to explore economic effects of changes in coal, oil and gas markets induced by climate-change mitigation policies. A large share of fossil fuel reserves and resources will be used in the absence of climate policy leading to atmospheric GHG concentrations well beyond a level of 550 ppm CO2-eq. This result holds independently of different assumptions about energy demand and fossil fuel availability. Achieving ambitious climate targets will drastically reduce fossil fuel consumption, in particular the consumption of coal. Conventional oil and gas as well as non-conventional oil reserves are still exhausted. We find the net present value of fossil fuel rent until 2100 at 30tril.US$ with a large share of oil and a small share of coal. This is reduced by 9 and 12tril.US$ to achieve climate stabilization at 550 and 450 ppm CO2-eq, respectively. This loss is, however, overcompensated by revenues from carbon pricing that are 21 and 32tril.US$, respectively. The overcompensation also holds under variations of energy demand and fossil fuel supply.