Carbon pricing is a recurrent theme in debates on climate policy. Discarded at the 2009 COP in Copenhagen, it remained part of deliberations for a climate agreement in subsequent years. As there is still much misunderstanding about the many reasons to implement a global carbon price, ideological resistance against it prospers. Here, we present the main arguments for carbon pricing, to stimulate a fair and well-informed discussion about it. These include considerations that have received little attention so far. We stress that a main reason to use carbon pricing is environmental effectiveness at a relatively low cost, which in turn contributes to enhance social and political acceptability of climate policy. This includes the property that corrected prices stimulate rapid environmental innovations. These arguments are underappreciated in the public debate, where pricing is frequently downplayed and the erroneous view that innovation policies are sufficient is widespread. Carbon pricing and technology policies are, though, largely complementary and thus are both needed for effective climate policy. We also comment on the complementarity of other instruments to carbon pricing. We further discuss distributional consequences of carbon pricing and present suggestions on how to address these. Other political economy issues that receive attention are lobbying, co-benefits, international policy coordination, motivational crowding in/out, and long-term commitment. The overview ends with reflections on implementing a global carbon price, whether through a carbon tax or emissions trading. The discussion goes beyond traditional arguments from environmental economics by including relevant insights from energy research and innovation studies as well. (C) 2017 The Authors. WIREs Climate Change published by Wiley Periodicals, Inc.