  Addressing the problem of fairness is crucial to safely use machine learning
algorithms to support decisions with a critical impact on people's lives such
as job hiring, child maltreatment, disease diagnosis, loan granting, etc.
Several notions of fairness have been defined and examined in the past decade,
such as statistical parity and equalized odds. The most recent fairness
notions, however, are causal-based and reflect the now widely accepted idea
that using causality is necessary to appropriately address the problem of
fairness. This paper examines an exhaustive list of causal-based fairness
notions and study their applicability in real-world scenarios. As the majority
of causal-based fairness notions are defined in terms of non-observable
quantities (e.g., interventions and counterfactuals), their deployment in
practice requires to compute or estimate those quantities using observational
data. This paper offers a comprehensive report of the different approaches to
infer causal quantities from observational data including identifiability
(Pearl's SCM framework) and estimation (potential outcome framework). The main
contributions of this survey paper are (1) a guideline to help selecting a
suitable fairness notion given a specific real-world scenario, and (2) a
ranking of the fairness notions according to Pearl's causation ladder
indicating how difficult it is to deploy each notion in practice.
