Big data comes in many forms and facets, from large volumes of structured and unstructured data (e.g., large image and video collections) to very heterogeneous collections with data in diferent formats and data models, and in a wide variety of applications - from data analytics and machine learning to business applications and personal information management. In each of these cases, specific support for data management, processing, and retrieval is essential. In this talk, we will give an overview of the various challenges of data management in the age of big data and present selected big data projects of the Databases and Information Systems Research Group at the University of Basel that address these challenges: the polystore database management system Polypheny and the full-stack multimedia retrieval system vitrivr.