Consumption of resources is rising rapidly, biodiversity is plummeting and just about every measure shows humans affecting Earth on a vast scale. Most of us accept the need for a more sustainable way to live, by reducing carbon emissions, developing renewable technology and increasing energy efficiency. But are these efforts to save the planet doomed? A growing band of experts are looking at figures like these and arguing that personal carbon virtue and collective environmentalism are futile as long as our economic system is built on the assumption of growth. The science tells us that if we are serious about saving Earth, we must reshape our economy. This, of course, is economic heresy. Growth to most economists is as essential as the air we breathe. They see no limits to that growth, ever. In recent weeks it has become clear just how terrified governments are of anything that threatens growth, as they pour billions of public money into a failing financial system. Amid the confusion, any challenge to the growth dogma needs to be looked at very carefully. This one is built on a long-standing question: how do we square Earth's finite resources with the fact that as the economy grows, the amount of natural resources needed to sustain that activity must grow too? It has taken all of human history for the economy to reach its current size. On current form it will take just two decades to double. In this special issue, New Scientist brings together key thinkers from politics, economics and philosophy who profoundly disagree with the growth dogma but agree with the scientists monitoring our fragile biosphere.