Poverty reduction is a key goal of the social policy of most European national governments. Apart from generating employment opportunities and promoting their generation, direct payments to qualifying individuals and households are the most important element of such policies. In this chapter, we study how and to what extent this expectation is satisfied by social transfers as a source of income. Our principal device is the comparison of poverty, as assessed by various indices, in the ‘real world’ (R-world), in which social transfers are regarded as one of the sources of income, and in the ‘alternative world’ (Aworld), in which all the social transfers are disregarded (discounted). The ideal system of social transfers would eradicate all poverty. This would entail raising the value of the equivalised household income (eHI) of each household classified as poor in the alternative world (A-poor) to the poverty standard. This ideal is clearly not attainable, even if the dispensers of social transfers had the intention to achieve it. First, future income from (self-)employment and other sources is not known, and so the level of social transfers has to be based on past income. Next, the real-world threshold (R-threshold) differs from the alternative-world threshold (A-threshold) if eHI of some households is raised from below the standard to above it. Further, social transfers include some payments not related to income directly, such as child support and disability entitlements. And finally, there is no single measure of poverty that could be used by the social transfer system for all its purposes.