Designing machine learning algorithms that are accurate yet fair, not discriminating based on any sensitive attribute, and also private, not revealing users’ personal information, has become of paramount importance for society to accept the widespread use of artificial intelligence (AI) for critical applications. In this thesis, we investigate the use of variational Information Bottleneck (IB) methods for fair and private machine learning. We present a novel fair representation learning method termed Rényi Fair Information Bottleneck (RFIB) which incorporates constraints for utility, fairness, and compactness of representation. In contrast to prior work, we consider both demographic parity and equalized odds as fairness constraints, allowing for a more nuanced satisfaction of both criteria. We use the Rényi divergence in developing a loss function involving classical IB measures and show that its parameter α provides an extra degree of freedom that results in performance benefits. Applying the method to image classification, we study the influence of the α parameter and two other tunable IB parameters on achieving utility/fairness trade-off goals, and evaluate it using various utility, fairness, and compound utility/fairness metrics on three different image datasets (EyePACS, CelebA, and FairFace), showing that RFIB outperforms current state-of-the-art approaches. Furthermore, we investigate how the problem of privacy relates to the problem of fairness and present a related method to jointly improve fairness and privacy termed Rényi Fair and Private Information Bottleneck (RFPIB). Using the Rényi divergence and IB measures, we develop a loss function designed to improve both privacy and multiple fairness metrics while also ensuring utility. Experimenting on the CelebA and EyePACS datasets, we study trade-offs between fairness, privacy, and utility. We significantly outperform a baseline ResNet50 network and show that tuning the Rényi divergence’s α parameter can be used to simultaneously achieve these three desired criteria.