The divergence of a geodesic metric space X is, roughly speaking, the rate of growth of the maximum length of geodesics in X - B(r) that join pairs of points on the r-sphere \partial B(r). For example, in the Euclidean plane, the divergence is linear since this quantity is half the circumference of a circle; but in the hyperbolic plane the divergence is exponential. The divergence of a finitely generated group is defined to be that of a Cayley graph; this is well-defined and therefore an invariant of the group. In this introductory talk, I will survey what is known about the divergence of groups which are the fundamental group of a compact non-positively curved cube complex.