Cryptocurrencies are gaining prominence among individuals and companies alike, resulting in the growing adoption of so-called cryptocurrency wallet applications, as these simplify carrying out transactions. These wallets are available in a myriad of different forms and specifications. For example, there are hardware and software wallets. The latter can be divided into mobile, web, and desktop wallets. All of them offer attackers various ways to exploit vulnerabilities and steal money from victims. It is hard to keep track of this multitude of options and thus choose the right cryptocurrency wallet. For this reason, in this thesis, we collect the findings from previous literature to provide an overview of the various attack surfaces, possible countermeasures, and further research. Our systematic study has shown that there is still a considerable variety of attack vectors, which we have divided into six subcategories, (i) Memory and Storage, (ii) Operating Systems, (iii) Software Layer, (iv) Network Layer, (v) Blockchain Protocol, and (vi) Others. Some of the identified vulnerabilities have currently no solutions at all or hardly applicable countermeasures. However, some are easy to fix and simple to implement. One of the essential measures is to raise awareness of the identified weaknesses and the associated mitigations, if any, among the involved stakeholders, including users, developers, and exchanges.