Abstract: The covering spectrum of a Riemannian manifold was first defined by Sormani-Wei in 2004. We will review the definition of this spectrum which roughly measures the size of holes in the space using a special sequence of convering spaces called delta covers. On compact spaces, the covering spectrum is a subset of the (1/2) length spectrum and is determined by the marked length spectrum. This is not true on complete noncompact manifold. In recent work with Wei, we have begun to prove related weaker theorems. To capture more information about complete manifolds we have defined two other spectra: the cut-off covering spectrum and the rescaled covering spectrum. The rescaled covering spectrum has some interesting properties on spaces like the one sheeted hyperboloid which are asymptotic to cones.