Entrepreneurs, enterprises, and governments are using distributed ledger technology (DLT) as a component of complex information systems, and therefore interoperability capabilities are required. Interoperating DLTs enables network effects, synergies and, similarly to the rise of the Internet, it unlocks the full potential of the technology. However, due to the novelty of the area, interoperability mechanisms (IM) are still not well understood, as interoperability is studied in silos. Consequently, choosing the proper IM for a use case is challenging. Our paper has three contributions: first, we systematically study the research area of DLT interoperability by dissecting and analyzing previous work. We study the logical separation of interoperability layers, how a DLT can connect to others (connection mode), the object of interoperation (interoperation mode), and propose a new categorization for IMs. Second, we propose the first interoperability assessment for DLTs that systematically evaluates the interoperability degree of an IM. This framework allows comparing the potentiality, compatibility, and performance among solutions. Finally, we propose two decision models to assist in choosing an IM, considering different requirements. The first decision model assists in choosing the infrastructure of an IM, while the second decision model assists in choosing its functionality.