Our planet is under ever increasing pressure from environmental degradation, biodiversity loss and climate change. If as a global society we are to respond to this we need to quantitatively assess the current state and future trends. Today, the planet’s vital signs are monitored extensively from space and from networks of ground-based sensors. In addition, over the past fifty years we have developed sophisticated numerical models of the Earth’s systems based on our understanding of physics, chemistry and biology. However, we are still limited in our ability to accurately predict future change, especially at the local scale that is most relevant for decision-making. In this talk I will outline a set of "grand challenge" problems and discuss various ways in which Machine Learning is starting to be deployed to advance our capacity to address these, in particular by combining our fundamental understanding of the Earth system processes with new knowledge gleaned from the vast planetary datasets.