The euro area sovereign debt crisis was, in part, the result of the institutional and legal design of the Economic and Monetary Union (EMU). The crisis highlighted the fact that, for EMU to be fully sustainable as a multilevel system of fiscal and economic governance, it should be able to address the following challenges: (1) enforcing fiscal discipline; (2) addressing structural inequalities between different euro area economies; and (3) preventing and countering asymmetric shocks in an efficient manner. These are challenges that all federal, multilevel or fiscally decentralized systems face when allocating fiscal powers to different levels of government, and when attempting to find a balance between excessive centralization/decentralization.Over the years, from its creation through the euro area sovereign debt crisis and its aftermath, EMU has evolved to address these problems in different ways. This paper analyses the evolution of the EU's multilevel system of fiscal governance in relation to these three challenges, showing that they have been only partially addressed. The paper argues that, if it were to address the three highlighted obstacles more fully, the EU would face a crucial choice between two ideal models of fiscal integration: The 'surveillance model', where Member States continue to maintain all taxing power and where the EU is an enforcer of discipline, and the 'classic fiscal federalism' model, where the EU acquires its own independent sphere of fiscal authority, and thus its own fiscal tools for macroeconomic stabilization. The paper has discussed how to articulate a classic system of fiscal federalism -- i.e., where different fiscal functions and instruments are attributed to different levels of government -- within the Union, and the problems that this raises.The main aim of this paper is to provide a clear overview of the obstacles facing EMU and, more importantly, of the two ideal models of further fiscal integration available to the Union. Furthermore, although it may seem counterintuitive, the paper will show that the surveillance model poses just as much of a threat to Member States' autonomy, and presents us with the same democratic legitimacy problems, as the classic fiscal federalism model. The danger is that, in an effort to avoid the radical changes that come with classic fiscal federalism, the euro area may be edging slowly towards the surveillance model without the necessary awareness and debate.