  Frustrated quantum magnets can harbor unconventional spin liquid ground
states in which the elementary magnetic moments fractionalize into new emergent
degrees of freedom. While the fractionalization of quantum numbers is one of
the recurring themes in modern condensed matter physics, it often remains a
challenge to devise a controlled analytical framework tracking this phenomenon.
A notable exception is the exactly solvable Kitaev model, in which spin degrees
of freedom fractionalize into Majorana fermions and a Z2 gauge field. Here we
discuss the physics of fractionalization in three-dimensional Kitaev models and
demonstrate that the itinerant Majorana fermions generically form a (semi)metal
which, depending on the underlying lattice structure, exhibits Majorana Fermi
surfaces, nodal lines or topologically protected Weyl nodes. We show that the
nature of these Majorana metals can be deduced from an elementary symmetry
analysis of the projective time-reversal and inversion symmetries for a given
lattice. This allows us to comprehensively classify the gapless spin liquids of
Kitaev models for the most elementary tricoordinated lattices in three
dimensions. We further expand this classification by addressing the effects of
time-reversal symmetry breaking and additional interactions.
