This chapter deals with an application of stochastic control or stochastic game methods to the design of optimal timing of climate policies. In the first part, we propose a stochastic control approach for a cost-benefit model that takes into account the uncertainty on the access to a backstop (clean) technology. In a second part, we show how this model can be extended to a game theoretic framework, assuming non-cooperative behavior of two groups of countries that are affected by climate change related damages induced by their joint greenhouse gas emissions. Finally we discuss the possibility of implementing successive control synthesis cycles preceded by learning cycles concerning climate sensitivity statistics.