In this chapter we shall briefly discuss Bloch constant problems in higher dimensions. Let B be the Euclidean unit ball in Cn. We shall be interested in subclasses of H(B), consisting of mappings from B into Cn for which there is a positive lower bound for the supremum of the radii of the schlicht balls in the image of all mappings in the given subclass. In particular we consider the set of Bloch mappings, although there is not as close a relationship as in one variable between Bloch constant problems for this class of mappings and Bloch constant problems for more general mappings.