Algorithmic and artificial intelligence techniques show immense potential to deepen our understanding of socioeconomic inequality and inform interventions designed to improve access to opportunity. Interventions aimed at historically underserved communities are made particularly challenging by the fact that disadvantage and inequality are multifaceted, notoriously difficult to measure, and reinforced by feedback loops in underlying structures. While great strides have been made in these areas -- from assigning seats in public schools to poverty mapping -- there remain many domains with major opportunities for further contributions and the prospect that we may be able to develop unified frameworks for applying computational insights to improve societal welfare. In this thesis, we develop algorithmic and computational techniques to address these issues through two types of interventions: one in the form of allocating scarce societal resources and the other in the form of improving access to information. We examine the ways in which techniques from algorithms, discrete optimization, mechanism design, and network and computational sciences can combat different forms of disadvantage, including susceptibility to income shocks, social segregation, and disparities in access to health information. We highlight opportunities for computing to play a role in fundamental social change. We close with a discussion on open questions in an emerging research area -- Mechanism Design for Social Good (MD4SG) -- around the use of algorithms, optimization, and mechanism design to address.