The Baum-Connes conjecture (as originally formulated by Baum and Connes) sees any group as if the group were exact. For decades mathematicians wondered whether non-exact groups exist. All the groups which occur in real life are exact. The Gromov monster groups, however, are non-exact. This talk explains how the Baum-Connes conjecture has to be reformulated to take into account the existence of non-exact groups. For exact groups, the reformulated conjecture is the same as the original conjecture. Is Baum-Connes true or false for SL(3, Z) ?????