A void in the expanding universe is modeled by a spherical Minkowski region in a Tolman dust spacetime which tends asymptotically to a Friedmann universe. It is found that (1) a void cannot exist in a universe of positive spatial curvature, (2) a nonexpanding void can be matched only to a parabolic exterior, (3) an expanding void requires an exterior region of negative spatial curvature. Detailed models of a nonexpanding void and of an expanding one are presented.