Digital Twins (DTs) are increasingly deployed across application domains, yet the treatment of trust-related issues remains unevenly addressed. To examine whether and how trust is discussed in the current landscape, we conducted a systematic review of existing DT review papers and a mapping of their abstracts. Seven trust-related challenges and seven trust-enhancing strategies were defined to guide the analysis, enabling the trust focus of each paper to be characterised. By aggregating the challenges and strategies referenced across domains, distinct patterns of emphasis were observed. With certain domains consistently sharing similar spectrum of trust concerns, four integration types, including human-centred, safety-critical, context-specific, and technologically-driven, were identified as emergent categories reflecting how trust is prioritised in different deployment contexts. Drawing on the characteristics of these types, several preliminary directions for future research were proposed. These include the development of trust-by-design principles to inform early-stage decision-making, the inclusion of trust metadata in platform schemas to prompt systematic developer consideration of trust factors, and the exploration of how architectural choices, such as federated DTs, influence user trust.