Socially Responsible Investments (SRI) is a category of investments which has developed considerably over the past years and it accounts for an increasing share of total investments. This trend has been accompanied (or maybe encouraged) by an increase in the number and diversification of sustainability (or SRI) indices. Up to date, the majority of the research concerning sustainability indices focuses on the evaluation of their financial performance or comparison to traditional indices. In this paper I would like to dig deeper into the nature of SRI stock indices, focusing on the most important ones currently available. I will analyse their composition and performance, and conduct a critical comparison between them. By means of this detailed analysis, I will try to understand what kind of information do SRI indices convey us. Moreover, since I will consider several indices, I will try to see whether my findings hold for all of them, highlighting in this way their potential shortcomings.