This paper studies the optimal reinsurance problem when risk is measured by a general risk measure. Necessary and sufficient optimality conditions are given for a wide family of risk measures, including deviation measures, expectation bounded risk measures and coherent measures of risk. The optimality conditions are used to verify whether the classical reinsurance contracts (quota-share, stop-loss) are optimal essentially, regardless of the risk measure used. The paper ends by particularizing the findings, so as to study in detail two deviation measures and the conditional value at risk.Research partially supported by "Welzia Management SGIIC SA", "RD_Sistemas SA", "Comunidad Autónoma de Madrid" (Spain), Grant s-0505/tic/000230, and "MEyC" (Spain), Grant SEJ2006-15401-C04-03Publicad