As machine learning powered decision-making becomes increasingly important in our daily lives, it is imperative to strive for fairness in the underlying data processing. While fairness may have different meaning for different people and will depend on the context, researchers have developed various notions of fairness in recent years. We propose a rigorous algorithmic framework for fair data representation based on optimal transport, which allows us to estimate the Pareto frontier (i.e., the curve characterizing the optimal tradeoff) between prediction error and statistical disparity. Our framework comes with several key advantages, such as computational efficiency as well the ability to preserve data privacy. Furthermore, we show under which conditions various notions of group fairness and individual fairness are (in)compatible. We demonstrate the applicability and validity of the proposed framework both in regression and classification problems.