The ineffectiveness of monetary policy to rapidly stem crises and revitalize the economy, in terms of growth of GNP and employment, has become increasingly evident, especially after the burst of the recent financial crisis. This is one of the reasons why an incredible number of innovative experiments in the monetary field have emerged in the last few years. Furthermore, ICT have opened new unprecedented possibilities for the development of decentralized payment systems, which can work reliably without needing intermediaries or a central authority. Since Nakamoto's famous white paper, crypto currencies such as Bitcoin, Litecoin or Faircoin have spread swiftly in recent years. They are increasingly drawing attention in the public debate, in particular thanks to its innovative underlying technologies which allow reliable peer-to-peer payments, without the need of intermediaries. The paper aims to explore the potential of crypto currencies, as well as to bring to light their limits and contradictions. In doing so, the authors will particularly focus on Bitcoin, understood as a benchmark for the entire sector. A first issue which is addressed is whether Bitcoin should be considered as a currency or as a particular kind of asset. In this regard, the authors bring to light a set of factors which are negatively affecting the possibility of Bitcoin to function as an effective means of payment, making it more similar to a highly speculative asset. A second section is focused on the factors that could explain Bitcoin volatility. In particular, the paper use empirical data showing that the variation in crypto currencies market prices is not concretely influenced by the decisions taken by the Federal Reserve and the European Central Bank. The authors also come to the conclusion that the value of Bitcoin mostly depends on financial conventions, arguing that the existence of a space for implementing monetary policy is essential to avoid crypto currencies to lose their transactional function. Following this argument, the paper analyses some other evident contradictions of Bitcoin, with particular attention to the issue of trust and to some limits deriving from the way it has been designed. Lastly, the authors propose a reflection about the features that a crypto currency project which aims to enable new forms of monetary sovereignty, and to build an alternative to the capitalistic monetary institutions, needs to have.