  In this survey article we will consider universal lower bounds on the volume
of a Riemannian manifold, given in terms of the volume of lower dimensional
objects (primarily the lengths of geodesics). By `universal' we mean without
curvature assumptions. The restriction to results with no (or only minimal)
curvature assumptions, although somewhat arbitrary, allows the survey to be
reasonably short. Although, even in this limited case the authors have left out
many interesting results.
