This article investigates the evolution of data quality issues from traditional structured data managed in relational databases to Big Data. In particular, the paper examines the nature of the relationship between Data Quality and several research coordinates that are relevant in Big Data, such as the variety of data types, data sources and application domains, focusing on maps, semi-structured texts, linked open data, sensor & sensor networks and official statistics. Consequently a set of structural characteristics is identified and a systematization of the a posteriori correlation between them and quality dimensions is provided. Finally, Big Data quality issues are considered in a conceptual framework suitable to map the evolution of the quality paradigm according to three core coordinates that are significant in the context of the Big Data phenomenon: the data type considered, the source of data, and the application domain. Thus, the framework allows ascertaining the relevant changes in data quality emerging with the Big Data phenomenon, through an integrative and theoretical literature review.