It is increasingly evident that widely-deployed machine learning models can lead to discriminatory outcomes and can exacerbate disparities in the training data. With the accelerating adoption of machine learning for real-world decision-making tasks, issues of bias and fairness in machine learning must be addressed. Our motivating thesis is that among a variety of emerging approaches, representation learning provides a unique toolset for evaluating and potentially mitigating unfairness. This tutorial presents existing research and proposes open problems at the intersection of representation learning and fairness. We will look at the (im)possibility of learning fair task-agnostic representations, connections between fairness and generalization performance, and the opportunity for leveraging tools from representation learning to implement algorithmic individual and group fairness, among others. The tutorial is designed to be accessible to a broad audience of machine learning practitioners, and the necessary background is a working knowledge of predictive machine learning.