Algorithmic fairness has attracted increasing attention in the machine learning community. Various definitions are proposed in the literature, but the differences and connections among them are not clearly addressed. In this paper, we review and reflect on various fairness notions previously proposed in machine learning literature, and make an attempt to draw connections to arguments in moral and political philosophy, especially theories of justice. We also consider fairness inquiries from a dynamic perspective, and further consider the long-term impact that is induced by current prediction and decision. In light of the differences in the characterized fairness, we present a flowchart that encompasses implicit assumptions and expected outcomes of different types of fairness inquiries on the data generating process, on the predicted outcome, and on the induced impact, respectively. This paper demonstrates the importance of matching the mission (which kind of fairness one would like to enforce) and the means (which spectrum of fairness analysis is of interest, what is the appropriate analyzing scheme) to fulfill the intended purpose.

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