  We review various features of interacting Abelian topological phases of
matter in two spatial dimensions, placing particular emphasis on fractional
Chern insulators (FCIs) and fractional topological insulators (FTIs). We
highlight aspects of these systems that challenge the intuition developed from
quantum Hall physics - for instance, FCIs are stable in the limit where the
interaction energy scale is much larger than the band gap, and FTIs can possess
fractionalized excitations in the bulk despite the absence of gapless edge
modes.
