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It is crucial to consider the social and ethical consequences of AI and ML based decisions for the safe and acceptable use of these emerging technologies. Fairness, in particular, guarantees that the ML decisions do not result in discrimination against individuals or minorities. Identifying and measuring reliably fairness/discrimination is better achieved using causality which considers the causal relation, beyond mere association, between the sensitive attribute (e.g. gender, race, religion, etc.) and the decision (e.g. job hiring, loan granting, etc.). The big impediment to the use of causality to address fairness, however, is the unavailability of the causal model (typically represented as a causal graph). Existing causal approaches to fairness in the literature do not address this problem and assume that the causal model is available. In this paper, we do not make such assumption and we review the major algorithms to discover causal relations from observable data. This study focuses on causal discovery and its impact on fairness. In particular, we show how different causal discovery approaches may result in different causal models and, most importantly, how even slight differences between causal models can have significant impact on fairness/discrimination conclusions. These results are consolidated by empirical analysis using synthetic and standard fairness benchmark datasets. The main goal of this study is to highlight the importance of the causal discovery step to appropriately address fairness using causality.