For several decades now, the problematic influence of economic interests on public health practices and regulation has gained growing attention. Several conceptualizations of these processes have been put forward, including conflict of interest (COI), capture, production of ignorance, and hegemony. Drawing on an analytical review of the literature and a comparison of the notions, this chapter reflects on these different conceptualizations, the historical conditions of their development, their analytical and political implications, and their benefits and drawbacks for the social sciences. We suggest that a comprehensive analysis of influence requires an articulation of COI, ignorance, and hegemony: COI both as a reflection of the multiple channels of influence the industry has developed and as a powerful means of making visible the double-bind of scientists, experts, and regulators; ignorance as a way of exploring the asymmetries and power gradients at stake in the production and non-production of knowledge; and hegemony as a reminder of the key role processes of market construction and diverse political economies play in the logic of influence.