Data Linkage is an important step that can provide valuable insights for evidence-based decision making, especially for crucial events. Performing sensible queries across heterogeneous databases containing millions of records is a complex task that requires a complete understanding of each contributing databases schema to define the structure of its information. The key aim is to approximate the structure and content of the induced data into a concise synopsis in order to extract and link meaningful data-driven facts. We identify such problems as four major research issues in Data Linkage: associated costs in pair-wise matching, record matching overheads, semantic flow of information restrictions, and single order classification limitations. In this paper, we give a literature review of research in Data Linkage. The purpose for this review is to establish a basic understanding of Data Linkage, and to discuss the background in the Data Linkage research domain. Particularly, we focus on the literature related to the recent advancements in Approximate Matching algorithms at Attribute Level and Structure Level. Their efficiency, functionality and limitations are critically analysed and open-ended problems have been exposed.