The Hall effect in single crystals of Cu ( RRR = 2312) and Cu containing 76, 172 and 1100 ppm Zn has been studied in the temperature range 4.2–80°K (i.e. through the low-field/high-field transition). The temperature dependence of the effect is given for H along [111], [110], [100], [211], and other directions which show either a single open orbit or all closed orbits. It is shown how the qualitative features of this dependence can be explained in terms of the known topology of the Fermi surface. Comparable results are also given for polycrystalline samples of Cu, and Cu with 78, and 940 ppm Zn. These indicate that of the singular topological features associated with the open Fermi surface of Cu only orbits of the four-cornered rosette and dog's bone type contribute to the Hall effect in a polycrystal. Some further evidence is given to support the view that the anomalous maximum in the temperature dependence of the effect in a polycrystal, which is centred at about 50°K, arises from the low-field/high-field transition.