  It was recently shown that nonsymmorphic space group symmetries can protect
novel surface states with hourglass-like dispersions. In this paper, we show
that such dispersions can also appear in the bulk of three-dimensional (3D)
systems which respect nonsymmorphic symmetries. Specifically, we construct 3D
lattice models featuring hourglass-like dispersions in the bulk, which are
protected by nonsymmorphic and time-reversal symmetries. We call such systems
hourglass semimetals, as they have point or line nodes associated with
hourglass-like dispersions. Hourglass nodal lines appear in glide-invariant
planes, while hourglass Weyl points can occur on screw-invariant axes. The Weyl
points and surface Fermi arcs in hourglass Weyl semimetals are stable against
weak perturbations breaking those nonsymmorphic symmetries. Our results may
shed light on searching for exotic Weyl semimetals in nonsymmorphic materials.
