Climate science regularly makes headlines in the media, usually after an extreme weather event or a disaster, or in the wake of campaigns by think tanks about the science of climate change. In this presentation, I discuss four specific challenges that are posed to climate scientist when communicating with the public: (i) The widening gap between the scientific literacy of the public and the communication literacy of the scientists; (ii), the multiplicity of scientific information conduits; (iii), information of, and under, uncertainty; and (iv), the requirement to be precise without using technical language. It turns out that these challenges are quite generic to science communication. Climate scientists have learned from the regular international assessments they perform under the auspices of the Intergovernmental Panel on Climate Change and have accumulated a collective experience of more than 20 years. In this presentation I discuss the most important lessons learned from this experience and their relevant for other science areas which are also frequently communicating with the media and the public.