Algorithms are used to make decisions in an ever-increasing number of socially consequential domains. From risk assessment tools in the criminal justice system to content moderation tools to assessments in hiring, algorithms play a key role in shaping the lives of people around the world. Algorithms offer many potential benefits: they are consistent, scalable, and can leverage more data than any human could reasonably consume. However, without careful consideration algorithmic decision-making also carries a number of risks, like replicating human biases, creating perverse incentives, and propagating misinformation. This thesis seeks to develop principles for the responsible deployment of algorithms in applications of societal concern, realizing their benefits while address- ing their potential harms. What does it mean to make decisions fairly? How do theoretical ideas about societal impacts manifest in practice? How do existing legal protections apply in algorithmic settings, and how can technical insights inform policy?In this thesis, we explore these questions from a variety of perspectives. Part II leverages theoretical models to surface challenges posed by algorithmic decision-making and potential avenues to overcome them. Part III incorporates models of behavior to better understand the interplay between algorithms and humans decisions. In Part IV, we explore how these insights manifest in practice, studying applications in employment and credit scoring contexts. We conclude in Part V with open directions for future research.