The fundamentals of climate change are well established: greenhouse gases warm the planet; their concentrations in the atmosphere are increasing; Earth has warmed, and is going to continue warming with a range of impacts. This article summarises the contents of a recent publication issued by the UK's Royal Society and the US National Academy of Sciences. The report aims to make clear what is known and where there is still developing understanding on climate change science. There are important discussions to be had and decisions that will need to be made about what actions individuals, governments and the world as a whole should take in response to climate change.