Since the mid-1970s, sub-Saharan candidates for migration to Europe have been confronted with increasingly stiff policy measures. This chapter explores how migration between Senegal and Europe has evolved in this context. Taking advantage of the retrospective nature of the data from the MAFE project (Migration between Africa and Europe) in addition to other available sources, it offers a unique quantitative account of the history of Senegalese migration. The results show that, between 1975 and 2008, there was neither a surge in out-migration (despite the widespread belief in an African invasion in Europe) nor the decline that might have been expected if restrictions had been effective. In fact, results tend in many ways to support the hypothesis that the effectiveness of restrictive policies is hampered by a number of unintended effects due to the ability of (would-be) migrants to adapt to new rules. Among these unintended effects are: the decline in intentions to return from Europe, the increase in attempts to migrate to Europe and the growth of irregular migration.