Machine learning is increasingly used to inform decision-making in sensitive situations where decisions have consequential effects on individuals’ lives. In these settings, in addition to requiring models to be accurate and robust, socially relevant values such as fairness, privacy, accountability, and explainability play an important role in the adoption and impact of said technologies. In this work, we focus on
algorithmic recourse
, which is concerned with providing
explanations
and
recommendations
to individuals who are unfavorably treated by automated decision-making systems. We first perform an extensive literature review, and align the efforts of many authors by presenting unified
definitions
,
formulations
, and
solutions
to recourse. Then, we provide an overview of the
prospective
research directions towards which the community may engage, challenging existing assumptions and making explicit connections to other ethical challenges such as security, privacy, and fairness.