Recommender systems are the algorithms which select, filter, and personalize content across many of the world's largest platforms and apps. As such, their positive and negative effects on individuals and on societies have been extensively theorized and studied. Our overarching question is how to ensure that recommender systems enact the values of the individuals and societies that they serve. Addressing this question in a principled fashion requires technical knowledge of recommender design and operation, and also critically depends on insights from diverse fields including social science, ethics, economics, psychology, policy, and law. This article is a multidisciplinary effort to synthesize theory and practice from different perspectives, with the goal of providing a shared language, articulating current design approaches, and identifying open problems. We collect a set of values that seem most relevant to recommender systems operating across different domains, and then examine them from the perspectives of current industry practice, measurement, product design, and policy approaches. Important open problems include multi-stakeholder processes for defining values and resolving trade-offs, better values-driven measurements, recommender controls that people use, non-behavioral algorithmic feedback, optimization for long-term outcomes, causal inference of recommender effects, academic-industry research collaborations, and interdisciplinary policy-making.