Is there such a process as "sustainable growth"? The term appears frequently in government reports and in company strategic plans. "Sustainable growth" holds out the tantalising prospect that a society can achieve the holy grail of sustainability - a modern term embracing alignment with environmental imperatives - without forgoing the benefits of economic expansion. These benefits include rising standards of living, full employment, increasing opportunities for investment or professional development - generally rising wealth for all. "Growth" is commonly used as a shorthand term for "economic growth" which relies upon geometrically expanding extraction and throughput of material resources, which is unsustainable in a finite planet, but there are forms of community advancement other than "growth" in a material sense. "Sustainability" implies a steady-state condition, not one built upon expansion or increasing throughput of material resources, but if it is based upon utilisation of renewable resources, then the steady-state condition may be satisfied. The paper explores the concept of "sustainable growth" by reviewing several scholarly attempts to explain the causes or consequences of economic growth. The paper touches on related questions such as: Is there any way of decoupling a rise in living standards from throughput of biophysical resources? Is it possible to have rising real wealth other than by accumulating more physical goods which means more demands upon the earth's resources? Can the contrasting views of science and economics on these questions be reconciled?