Social Europe, or the social dimension of the European Union (EU), has been receiving increasing attention in academic debates. This special issue introduction discusses Social Europe through the analytical framework of multi‐level governance while asking, perhaps controversially, whether Social Europe has the potential to become a fully‐fledged welfare state. This introduction also summarises the articles included in this special issue which focus on different governance levels, including EU institutions, member states, national parties, economic sectors, workers and the general public. On this basis, the introduction identifies sources of challenges and opportunities for Social Europe from various levels of governance. We conclude that the needs and demands become more diverse when we move from European institutions to the citizens. Notably, obstacles from one governance level often carry over to another governance level. Consequently, it becomes much more difficult to design welfare policies on the EU level that work for everyone. While a more evolved EU‐level welfare state may be possible in the future, substantial obstacles make it difficult to achieve in the short run. Hence, future research should examine the multi‐level structure of Social Europe in more detail to better grasp what Social Europe can and cannot deliver and why. Such research is not only relevant in the European Union but also in other multi‐level governance systems across the world.