This conceptual paper addresses the capabilities offered by big data analytics (BDA), critical in turbulent environments, in the context of the Industry 4.0 revolution. BDA enhances organizational agility, as it is highly valuable for the identification of opportunities and threats (i.e. the sensing process of agility); however, with the exception of aiding decision-making tools, seizing its benefits for reacting (i.e. responding) is more difficult without organizational adaptation. Hence, the changes required to exploit the full capabilities offered by BDA, particularly at the organizational level, are considerable. From a theoretical perspective, through a narrative literature review, this paper highlights several possibilities of organizational changes for enhancing a company’s agility and leveraging BDA to achieve enhanced performance in turbulent contexts. The findings are then related to three organizational theories. This work ends in a conceptual model and several research paths for future studies. From a managerial perspective, this paper highlights, through several examples, the importance of top management’s role in achieving the necessary organizational changes to enhance the companies’ responding capabilities.