The Internet of Things (IoT), personal and wearable devices, and continuous advances in data-gathering techniques have significantly increased the amount of relevant data that can be leveraged for innovative real-time, data-driven applications. Digital Twins (DTs) are virtual representations of physical objects which are fully integrated and in which the automatic data exchange occurs in a bidirectional way. DTs and big data are mutually reinforcing technologies since huge volumes of data representing the physical/virtual worlds are collected, transformed, and generated through models to aggregate value to the business. Modern DTs follow a five-component architecture, which includes a Data Management (DM) component that bridges a physical system, a mirrored virtual one, and services components. However, there is no clarity on the functionality required for the DM component. This work presents a Systematic Literature Review on DM issues and proposed solutions in the DT context. We analyzed DM under the big data value chain activities, highlighting key issues to be addressed: data heterogeneity, interoperability, integration, data search/discovery, and quality. In addition to surveying existing solutions for handling these issues, we contextualized them in the domain and function for which the DT was proposed, the type of data dealt with, and the technical infrastructure. The compilation of these solutions sheds light on the functionality of the DM component in a DT, trends, and opportunities. Our main findings revealed that the maturity level assumed for the DM component is at an early stage. The most mature solutions were proposed for the industry domain, and many of them assume humans as the ultimate information consumers. Data integration is the prevalent DM issue addressed due to the bridging role of the DM component, and cloud computing is the key implementation technology. Among the research opportunities are reference data management architectures, adoption of industry standards and ontologies, interoperability among distinct DTs, the development of agnostic standard implementations, and data provenance mechanisms.