This chapter seeks to demonstrate that EU politics deeply and directly affects the daily life of all its citizens. It creates both, opportunities and constraints for member state governments and people. They cannot be disentangled because the EU deeply penetrates domestic politics in member states. In essence, domestic politics cannot be understood without the inescapable context of EU politics. The EU effectively transformed its members. EU politics therefore raises two key puzzles that political scientists sought to reckon with. Why did Europeans integrate into the EU in the first place when its effects were so ambiguous? How did Europeans respond and sought to protect themselves against undesirable penetration, when the EU hit home? The answer to both questions will allow to discuss the question of how democratically legitimate EU politics can be.