Competition law ensures the proper functioning of the market by countering the negative effects of corporate power. It traditionally measures this power and its effects based on economic parameters. However, the big corporations that shape our current digital platform economy wield power that significantly transcends the economic domain, reaching into politics, and the social and personal spheres. Their power manifests itself not just instrumentally, but also structurally and discursively. It therefore challenges traditional assumptions underlying competition law. This chapter proposes a refined taxonomy of power and recommends a new vocabulary to adequately understand and respond to big tech's ‘Modern Bigness.’