Big Data is based on the vision of providing users and applications with a more complete picture of the reality supported and mediated by data. This vision comes with the inherent price of data variety, i.e. data which is semantically heterogeneous, poorly structured, complex and with data quality issues. Despite the hype on technologies targeting data volume and velocity, solutions for coping with data variety remain fragmented and with limited adoption. In this talk we will focus on emerging data management approaches, supported by semantic technologies, to cope with data variety. We will provide a broad overview of semantic computing approaches and how they can be applied to data management challenges within organizations today. This talk will allow the audience to have a glimpse into the next-generation, Big Data-driven information systems.