What are the effects of supply-side climate policies in the oil market? We use global company-level data to estimate the impact of 84 reforms of production taxes between 2000 and 2019 on oil production, exploration, and discoveries. We find that higher taxes primarily reduce companies’ exploration expenditures and oil discoveries, and also reduce short-term production of unconventional oil. We then quantify the implications for the oil market using a short- and medium-term dynamic model over the period 2020–2100. Imposing a global climate royalty surcharge of 20 percentage points on oil producers reduces average annual emissions from oil by 5–7 percent in the first five years, and 9–20 percent in the medium term. If only OECD countries adopt this policy, 47–73 percent of the total emission reductions would be offset by increased production in non-OECD countries in the medium term.