  Recently there has been much effort in understanding topological phases of
matter with gapless bulk excitations, which are characterized by topological
invariants and protected intrinsic boundary states. Here we show that
topological semimetals of Majorana fermions arise in exactly solvable Kitaev
spin models on a series of three dimensional lattices. The ground states of
these models are quantum spin liquids with gapless nodal spectra of bulk
Majorana fermion excitations. It is shown that these phases are topologically
stable as long as certain discrete symmetries are protected. The corresponding
topological indices and the gapless boundary states are explicitly computed to
support these results. In contrast to previous studies of non-interacting
systems, the phases discussed in this work are novel examples of gapless
topological phases in interacting spin systems.
