The idea of a global carbon price has been a recurrent theme in debates on international climate policy. Discarded at the Conference of Parties (COP) of Copenhagen in 2009, it remained part of deliberations for a climate agreement in subsequent years. Unfortunately, there is still much misunderstanding about the reasons for implementing a global carbon price. As a result, ideological and political resistance against it prospers. The document presents the main arguments in favor of a carbon price to stimulate a fair and well-informed discussion about climate policy instruments. This includes arguments that have received surprisingly little attention so far. It is stressed that a main reason to use carbon pricing is environmental effectiveness, so not only economic efficiency (including the special case of cost-effectiveness). In addition, it provide ideas on how to implement a uniform global carbon price, whether using a carbon tax or emissions trading.