Cryptographic protocols such as TLS rely on Public Key Infrastructure (PKI) to provide privacy to the users on the web. In traditional PKI a certain number of Certificate Authorities (CA) issue certificates which affirm that the CA verified the public key binding. However, since CAs in numerous cases behaved maliciously and issued unauthorized certificates, alternatives to traditional PKI model are being researched. Promising alternative is a blockchain technology which seems to be suitable for the implementation of PKIs: A blockchain is decentralized usually with only a few trust anchors. Data has to pass a consensus procedure before it becomes part of the state of the blockchain. Hence, blockchain offers a decentralized alternative to current CA-based PKI model. In this thesis we survey the current state of research into PKIs based on blockchains. Firstly, we present PKI and blockchain, two integral parts of such systems. There we concentrate on PKI models and blockchain platforms that are relevant for the existing blockchain-based PKI proposals. We then introduce, classify, and present PKI systems based on blockchains. In the following chapter we discuss security properties, prospects for adoption, underlying blockchains, and distinctive features of blockchain-based PKI systems which are in the course of this compared to each other, to conventional PKIs, and its extensions. In the end, we introduce TKI, a PKI system developed on permissionless Ethereum blockchain that extends CA-based PKI and combines it with a Web of Trust architecture.