The third generation of Distributed Ledger Technology (DLT) allows advanced and various applications with Smart Contracts in an environment of interconnected organizations, external entities and real-world processes. Many organizations operate in such an environment and are engaged with compliance requirements, such as laws and regulation. This leads to a multitude of challenges for organizations. For the most part, organizations lack a general understanding of this emerging technology regarding the use in compliance. Therefore, we present in this work, based on a literature review, an overview what challenges DLT is able to address and what risks could emerge through the use of DLT in this area of application. Moreover, we differentiate the effects of single DLT characteristics addressing different compliance challenges and discuss important controversial aspects (e.g. integrity of data vs. GDPR requirements). We further discuss the suitability of the most common DLT designs, Ethereum and Hyperledger, in the context of compliance and provide a brief outlook on illustrative business use cases for DLT in compliance.