 On the surface, the incompatibility between general relativity and quantum theory might seem rather trivial. Why not just follow the model of QED and quantize the gravitational field, similar to the way in which the electromagnetic field was quantized? This is more or less the path that was taken, but it encounters extraordinary difficulties. Some physicists consider these to be ‘merely’ technical difficulties, having to do with the non-renormalizability of the gravitational interaction and the consequent failure of the perturbative methods which have proven effective in ordinary quantum field theories. However, these technical problems are closely related to a set of daunting conceptual difficulties, of interest to both physicists and philosophers.