Let d be a fixed positive number. It is well-known that locally around a randomly chosen vertex, the random graph G(n,d/n) is merely a tree with high probability. Nonetheless, the chromatic number of the random graph may be very large. The aim of this talk is to examine the interplay of "local" and "global" effects in the random graph colouring problem. The talk is based on joint work with Charilaos Efthymiou and Nor Jaafari.