  The theory of topological insulators and superconductors has mostly focused
on non-interacting and gapped systems. This review article discusses
topological phases that are either gapless or interacting. We discuss recent
progress in identifying gapless systems with stable topological properties
(such as novel surface states), using Weyl semimetals as an illustration. We
then review recent progress in describing topological phases of interacting
gapped systems. We explain how new types of edge states can be stabilized by
interactions and symmetry, even though the bulk has only conventional
excitations and no topological order of the kind associated with Fractional
Quantum Hall states.
