We explore cost-efficient scenarios for reaching climate targets for the transportation sectors in the EU and Sweden, covering both passenger and freight transport. Our focus is on the relative contributions to emissions reductions from electrification, biofuels and traffic reduction. Information about cost-efficient scenarios can serve as roadmaps to reach given targets. This is important not only for designing climate policies; it also has implications for traffic planning, biofuel production planning and the transformation of the vehicle manufacturing industry. Our results indicate that electrification is by far the most important factor for reaching the climate targets. With the recent EU vehicle regulations in place, it is possible to reach the climate targets at a moderate cost; with slow electrification, the long-run targets are virtually impossible to reach. Assuming that EU emission standards are binding, reaching the targets also requires considerable amounts of biofuel, especially in the short and medium term. Traffic reduction contributes only marginally to reduced emissions. Hence, other negative externalities from road traffic need to be handled by other policy measures; climate policy only makes a marginal contribution to reducing other traffic externalities.