For some types of bounding volume (OBB and convex polyhedra), an effective check is that of the separating axis theorem. The idea here is that, if there exists an axis by which the objects do not overlap, then the objects do not intersect. Usually the axes checked are those of the basic axes for the volumes (the unit axes in the case of an AABB, or the 3 base axes from each OBB in the case of OBBs). Often, this is followed by also checking the cross-products of the previous axes (one axis from each object).