The increasing use of data-driven decision support systems in industry and governments is accompanied by the discovery of a plethora of bias and unfairness issues in the outputs of these systems. Multiple computer science communities, and especially machine learning, have started to tackle this problem, often developing algorithmic solutions to mitigate biases to obtain fairer outputs. However, one of the core underlying causes for unfairness is bias in training data which is not fully covered by such approaches. Especially, bias in data is not yet a central topic in data engineering and management research. We survey research on bias and unfairness in several computer science domains, distinguishing between data management publications and other domains. This covers the creation of fairness metrics, fairness identification, and mitigation methods, software engineering approaches and biases in crowdsourcing activities. We identify relevant research gaps and show which data management activities could be repurposed to handle biases and which ones might reinforce such biases. In the second part, we argue for a novel data-centered approach overcoming the limitations of current algorithmic-centered methods. This approach focuses on eliciting and enforcing fairness requirements and constraints on data that systems are trained, validated, and used on. We argue for the need to extend database management systems to handle such constraints and mitigation methods. We discuss the associated future research directions regarding algorithms, formalization, modelling, users, and systems.