Developments in Artificial Intelligence (AI) and Distributed Ledger Technology (DLT) currently lead to lively debates in academia and practice. AI processes data to perform tasks that were previously thought possible only for humans. DLT has the potential to create consensus over data among a group of participants in uncertain environments. In recent research, both technologies are used in similar and even the same systems. Examples include the design of secure distributed ledgers or the creation of allied learning systems distributed across multiple nodes. This can lead to technological convergence, which in the past, has paved the way for major innovations in information technology. Previous work highlights several potential benefits of the convergence of AI and DLT but only provides a limited theoretical framework to describe upcoming real-world integration cases of both technologies. We aim to contribute by conducting a systematic literature review on previous work and providing rigorously derived future research opportunities. This work helps researchers active in AI or DLT to overcome current limitations in their field, and practitioners to develop systems along with the convergence of both technologies.