In recent years, the emerging Digital Twin (DT) technology is playing a key role in fostering the transition towards the Industry 4.0. DTs, representing virtual replicas of physical objects, products or processes established thanks to a bidirectional continuous flow of information between the physical and the virtual world, are currently adopted in multiple domains such as manufacturing, aerospace, automotive, energy, construction, smart cities and smart mobility, etc.. DTs live together with the physical system they replicate, receiving the same data and often triggering specific control actions that directly impact on the real system status. When dealing with DTs of complex Cyber-Physical Systems (CPSs), the data sources may be heterogeneous and untrustworthy, which requires the DT to be able to address security issues related to data in transit from/to the physical twin and data at rest. A possible way to address these data security issues consists in adopting Distributed Ledger Technologies (DLTs) which provide several security guarantees on data through cryptographic hashing techniques. In this work, we present a three-fold contribution: (i) we discuss the results of a Systematic Literature Review (SLR) on the state-of-the-art of the research related to the integration between DLT and Digital Twins, aimed at clarifying relevant aspects such as, among others, what is the favourite DLT choice in existing proposals or what is the type of DT-related information to store on-chain; (ii) leveraging the SLR results and other related research, we propose an architectural framework for the integration of DT and DLTs (more specifically, blockchains); (iii) we validate the proposed architecture by means of two proof-of-concept implementations leveraging different technological stacks and taking into account two different operational scenarios. Finally, we conduct a requirements coverage analysis and compare the PoCs through a coverage matrix.