The increasing number of sovereign wealth funds (SWFs) and the growth in the value of their assets are among the main current trends in the global financial markets. The governments of recipient States have voiced their concerns, contending that SWFs are financial vehicles used by States to pursue general public aims but acting like private economic agents. The question this contribution tackles is whether SWFs, as 'sovereign' investment vehicles, come within the scope of international and national rules on sovereign immunity. As a starting point, the definition of 'sovereign States' given by immunity legal regimes will be investigated in order to define in which circumstances SWFs meet it. Next the issue of SWFs' immunity from adjudication will be ascertained. In this regard, the main point is whether SWFs investments are to be understood as actions engaged in within the exercise of sovereign authority, or as mere commercial activities, over which immunity from judgement on the merits is removed. As it may not be excluded that courts render judgements against SWFs, the rules on immunity from pre-judgement and post-judgement measures of constraint are to be considered, so as to identify the property against which jurisdictional rulings may be enforced. The enquiry mainly focuses on the rules established under the UN and Council of Europe conventions; the content and practice under national regimes is also considered, mainly the US Foreign Sovereign Immunities Act and the UK State Immunity Act. The main result is that there is no univocal answer to the question whether rules on sovereign immunity are helpful in overcoming the contradiction between the different but complementary public and private nature of SWFs. The form through which funds have been established and the content of the specific legal regime on whose basis courts have to judge in their regard are fundamental variables, and their combination in each case may lead to different results in terms of immunity from both the adjudicative process and enforcement measures.