Since the financial crisis spreads around the world, there is a growing concern about the sustainability of public debt, which focuses on the path or level of public debt that is necessary for ruling out a fiscal crisis. This paper aims to provide an overview of research on public debt sustainability. Relative conceptions are introduced and redefined at first, and there are two approaches we comment to assessing sustainability of public debt, one is testing whether the IBC holds, and the other is using indicators to know how far public debt departs from sustainability. Then we introduce some opinions different from, but relative to the sustainability of public debt. Finally the advantages of those researches and future tasks are discussed.