The earthquake cycle is poorly understood. Earthquakes continue to occur on previously unrecognized faults. Earthquake prediction seems impossible. These remain the facts despite nearly 100 years of intensive study since the earthquake cycle was first conceptualized. Using data acquired from satellites in orbit 800 km above the Earth, a new technique, radar interferometry (InSAR), has the potential to solve these problems. For the first time, detailed maps of the warping of the Earth's surface during the earthquake cycle can be obtained with a spatial resolution of a few tens of metres and a precision of a few millimetres. InSAR does not need equipment on the ground or expensive field campaigns, so it can gather crucial data on earthquakes and the seismic cycle from some of the remotest areas of the planet. In this article, I review some of the remarkable observations of the earthquake cycle already made using radar interferometry and speculate on breakthroughs that are tantalizingly close.