Carbon emissions from energy production and industrial processes are deeply entrenched in our economies. To mitigate the risk of catastrophic climate change they need to be reduced to a fraction of todays level. The challenge for climate policy is to deliver these emissions reductions. Carbon prices play an essential role. They create incentives for all players in the economy to look for their opportunity to tackle carbon without committing a foul against economic performance or social wellbeing. Emissions trading is a viable approach to deliver carbon prices. The details of the implementation of this approach deserve particular attention, as they guide the investment strategies of households, firms and technology developers. The experience with the European Union Emissions Trading Scheme shows a clear focus on delivering the price is important. Any additional policy objectives should be pursued with other instruments. Ambitious countries will implement high carbon prices in order to challenge their industries to be the first to develop low-carbon strategies and technologies. But will industries accept the challenge, or will they relocate to countries where carbon prices are lower? Detailed analysis suggests that concerns only apply to few sub-sectors where they can be addressed through specific instruments.