SoK: Communication across distributed ledgers Since the inception of Bitcoin, a plethora of distributed ledgers differing in design and purpose has been created. While by design, blockchains provide no means to securely communicate with external systems, numerous attempts towards trustless cross-chain communication have been proposed over the years. Today, cross-chain communication (CCC) plays a fundamental role in cryptocurrency exchanges, scalability efforts via sharding, extension of existing systems through sidechains, and bootstrapping of new blockchains. Unfortunately, existing proposals are designed ad-hoc for specific use-cases, making it hard to gain confidence in their correctness and composability. We provide the first systematic exposition of cross-chain communication protocols. We formalize the underlying research problem and show that CCC is impossible without a trusted third party, contrary to common beliefs in the blockchain community. With this result in mind, we develop a framework to design new and evaluate existing CCC protocols, focusing on the inherent trust assumptions thereof, and derive a classification covering the field of cross-chain communication to date. We conclude by discussing open challenges for CCC research and the implications of interoperability on the security and privacy of blockchains. 12675 3-36 3-36 Springer Nature