Climate change has already reached crisis levels, and the threat of climate catastrophe is only too real. I will begin by briefly reviewing global warming and climate change in terms of its physical causes, describe the importance of feedbacks, and then go on to describe the expected physical impacts of climate change. I will briefly describe the biological impacts too, focusing on the impending collapse of coral reef ecosystems, because of what this tells us about the onset of tipping points, and to introduce the concept of ‘wobble and tip’. Then I will focus the rest of the talk on the cryosphere, especially the Greenland ice sheet, to develop the concept of tipping points in more detail. In particular, I will argue that Greenland ice sheet has already passed two tipping points, one associated with global ocean warming, and the other associated with global warming of the atmosphere.