Greenhouse gas emissions are a negative externality because private decisions to burn fossil fuels do not fully reflect the climate damages imposed on others. This paper compares two market-based instruments designed to correct that failure: carbon taxes, which fix the price of emissions and allow quantities to adjust, and cap-and-trade systems, which fix the emissions quantity and allow the permit price to adjust. The case studies are the European Union Emissions Trading System (EU ETS) and Sweden's national carbon tax. The review finds that both instruments can generate meaningful emissions reductions when their coverage is broad, their carbon price is material, and exemptions are limited. Peer-reviewed evidence estimates that the EU ETS reduced regulated manufacturing emissions by 14% in Phase I and 16.3% in Phase II, and avoided about 1.2 billion tonnes of CO2 between 2008 and 2016. For Sweden, synthetic-control and firm-level studies estimate an almost 11% transport-sector reduction and large manufacturing-sector responses to carbon pricing. The main conclusion is not that one instrument is universally superior. Design details - coverage, revenue use, price stability, exemptions, and trade-exposure protections - largely determine efficiency, equity, and political durability.