Since the emergence of the Bitcoin cryptocurrency, the blockchain technology has become the new Internet tool with which researchers claim to be able to solve any existing online problem. From immutable log ledger applications to authorisation systems applications, the current technological consensus implies that most of Internet problems could be effectively solved by deploying some form of blockchain environment. Regardless this ‘consensus’, there are decentralised Internet-based applications on which blockchain technology can actually solve several problems and improve the functionality of these applications. The development of these new blockchain-based solutions is grouped into a new paradigm called Blockchain 3.0 and its concepts go far beyond the well-known cryptocurrencies. In this paper, we study the current trends in the application of blockchain on the paradigm of Public Key Infrastructures (PKI). In particular, we focus on how these current trends can guide the exploration of a fully Decentralised Identity System, with blockchain as be part of the core technology.