  Human lives are increasingly being affected by the outcomes of automated
decision-making systems and it is essential for the latter to be, not only
accurate, but also fair. The literature of algorithmic fairness has grown
considerably over the last decade, where most of the approaches are evaluated
under the strong assumption that the train and test samples are independently
and identically drawn from the same underlying distribution. However, in
practice, dissimilarity between the training and deployment environments
exists, which compromises the performance of the decision-making algorithm as
well as its fairness guarantees in the deployment data. There is an emergent
research line that studies how to preserve fairness guarantees when the data
generating processes differ between the source (train) and target (test)
domains, which is growing remarkably. With this survey, we aim to provide a
wide and unifying overview on the topic. For such purpose, we propose a
taxonomy of the existing approaches for fair classification under distribution
shift, highlight benchmarking alternatives, point out the relation with other
similar research fields and eventually, identify future venues of research.
