The subject of blockchain technology and cryptocurrencies is very topical and popular in business circles. However, the scholarly literature reveals a literature gap and not enough scientific findings regarding these new financial technologies, especially in Islamic banking-related literature. The main objective of this paper is to survey, identify, and qualitatively analyze all the relevant published studies in the area of Islamic banking and new financial technologies (such as the blockchain and cryptocurrencies) thus far, as well as to present their findings and to draw conclusions regarding the state of the art in Islamic banking-related scholarly literature. Another goal is to provide a theoretical background to the concept of Islamic Banking and Finance (IBF) as well as to blockchain technology. Systematic literature reviews (SLRs) have been established as a stepping stone for the presentation of the state of the art in a scientific area to the academic community. Therefore, an SLR with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines has been applied combining electronic and manual searches to identify relevant studies using keywords “BLOCKCHAIN” and/or “CRYPTOCURRENCY” and/or “BITCOIN” and “ISLAMIC BANKING.” In the first stage, the selection of the surveyed scientific databases has been conducted, and these are the well-renowned global scientific databases Scopus and Web of Science, with no restrictions to language, date of publication, or study design. In this stage of the research, an electronic survey of these databases is undergone with the abovementioned keywords. In the second stage, a manual survey and initial screening (i.e., a review of the abstracts in order to establish if they are relevant to this SLR) of the papers is conducted. The third stage of the research (i.e., the eligibility phase) eliminated articles after a full-text eligibility decision had been made. The last, fourth stage of the research (the inclusion stage) includes a quantitative and qualitative analysis of the included relevant published papers. A detailed presentation of the included studies and their findings are thereafter presented in a narrative synthesis. Finally, specific subjects of research have been identified, and suggestions and guidelines for future work are provided. The scientific and practical contributions of this study are twofold. First, the state of Islamic banking in innovation and new financial technologies is presented, and second, it provides crucial information regarding the application of blockchain and cryptocurrencies in Islamic banking, which is valuable to regulatory bodies, governments, and potential investors.