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The purpose of this paper is to analyze the context and attack surface of a variety of security breaches and attacks on cryptocurrency blockchains. For many different types of blockchain attacks, such as distributed denial-of-service (DDoS) attacks and majority (51%) attacks, there is very little literature investigating and comparing particular attack instances as opposed to focusing on general theoretical studies and mitigation techniques. The attacks investigated here include a series of DDoS attacks on the Bitfinex cryptocurrency exchange and a group of instances of the 51% attack on thirteen different cryptocurrency blockchains. The goal of this research is to find traits in the context and attack surface that exacerbate the losses caused by certain attacks as opposed to others. It will then propose solutions and mitigation techniques based on the circumstances of the cases where the impact of the attack was less serious.