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Data sets and statistics about groups of individuals are increasingly collected and released, feeding many optimization and learning algorithms. In many cases, the released data contain sensitive information whose privacy is strictly regulated. For example, in the U.S., the census data is regulated under Title 13, which requires that no individual be identified from any data released by the Census Bureau. In Europe, data release is regulated according to the General Data Protection Regulation, which addresses the control and transfer of personal data. Differential privacy has emerged as the de-facto standard to protect data privacy. In a nutshell, differentially private algorithms protect an individual’s data by injecting random noise into the output of a computation that involves such data. While this process ensures privacy, it also impacts the quality of data analysis, and, when private data sets are used as inputs to complex machine learning or optimization tasks, they may produce results that are fundamentally different from those obtained on the original data and even rise unintended bias and fairness concerns. In this talk, I will first focus on the challenge of releasing privacy-preserving data sets for complex data analysis tasks. I will introduce the notion of Constrained-based Differential Privacy (C-DP), which allows casting the data release problem to an optimization problem whose goal is to preserve the salient features of the original data. I will review several applications of C-DP in the context of very large hierarchical census data, data streams, energy systems, and in the design of federated data-sharing protocols. Next, I will discuss how errors induced by differential privacy algorithms may propagate within a decision problem causing biases and fairness issues. This is particularly important as privacy-preserving data is often used for critical decision processes, including the allocation of funds and benefits to states and jurisdictions, which ideally should be fair and unbiased. Finally, I will conclude with a roadmap to future work and some open questions.