In this talk, I will present some recent results in the entanglement
entropy of gapped ground states. In particular, I will focus on the
following two results:

1) The topological entanglement entropy for some of the known topological
states with long-range entanglement in three and higher dimensions has an
interesting dependence on the Betti numbers of the boundary manifold
defined by the entanglement cut.

2) In contrast to the familiar result in two dimensions, a size
independent constant contribution to the entanglement entropy can appear
for non-topological phases in any odd spatial dimension.