After the huge debt increases in the 1940s, due to the WWII, and in the 1980s due to the emerging markets’ debt crises, the debt overhang problem is once again at the center of the academic and political debate because of the recent debt crisis that affected the European countries in 2009. The debt overhang theory explains how an high level of debt distorts the optimal investment decisions and reduces government’s incentives, in the debtor country, to undertake the necessary "adjustment policies". A huge literature focuses on the negative effects deriving from a debt overhang condition. In particular, this kind of literature has been mostly used to describe and to study poor and less developed countries. Nowadays instead, the situation is quite different with the Greek case that represents a very peculiar and never experienced situation. Chapter 1 of the thesis starts with an introduction of the sovereign debt overhang problem. Then, since the aim is to study the possible policy interventions able to solve it, the focus is posed on sovereign debt restructuring as a resolution mechanism. A relief intervention can be considered, indeed, as a way to reduce the debt burden for a country struggling with an high level of debt. Descriptions of the restructuring process, of the macroeconomic consequences and of the Greek case are then provided in this chapter in addition to some stylised facts and an event analysis useful to communicate the main messages. In the past, several different strategies of debt restructuring have been implemented and the consequences they produced were often different case by case. It is then interesting to study the effectiveness of the several options that can be used to restructure public debt. For this reason, a very simple theoretical model is developed in Chapter 2 in order to study three different strategies that can be used to solve a sovereign debt overhang problem. In particular, two strategies are based on a debt restructuring process, via face value reduction or rescheduling, whereas a third one is based on conditional-additional official lending. This strategy relies on the idea that the debtor country can benefit of new lending from the official sector, in order to undertake a larger amount of investment. The aim of the model is to represent schematically the functioning of the three restructuring processes to gain insights into their differences and to study their consequences in term of incentives to invest in a "troubled country". An empirical evidence of the debt overhang hypothesis is then provided in Chapter 3. The combination of the sovereign debt crisis of 2009 and the fiscal consolidation policies implemented as a result, makes indeed interesting to study this hypothesis in Europe. The Chapter exploits then a panel dataset for the European countries, between 1995 and 2015, in order to examine the extent to which increased levels of public debt have led to reduced public investment. We start the analysis from basic POLS models and then we expand it gradually to FE, IV and GMM estimation models. The results validate the debt overhang hypothesis and remain robust across various model specifications.