This paper explores how the concept of market power is being applied and adapted to digital markets, as well as the implications for competition policy. First, based on competition authority decisions and academic literature, it identifies the main contributors to market power in digital markets, including the role of network effects, economies of scale and scope, data, multi-homing and switching costs. The paper also considers whether these contributors are unique to digital markets, and some of the conceptual questions authorities have faced in assessing digital firms’ market power. Next, this paper reviews a range of concepts and terms recently applied to digital market dynamics that are related to market power. This includes particular types of “power” held by firms in digital markets (e.g. bottleneck power), and designations developed to capture the influence of specific firms in the context of new regulatory initiatives (e.g. gatekeepers). Finally, the paper considers several competition policy challenges related to market power in the digital era, including questions about the relationship between new regulatory concepts related to market power and established enforcement concepts such as dominance. It also highlights the risk of growing divergences in the application of new regulatory designations. This paper concludes that market power should remain a core guiding principle as the competition policy community faces these challenges.