  The theory of anyon systems, as modular functors topologically and unitary
modular tensor categories algebraically, is mature. To go beyond anyons, our
first step is the interplay of anyons with conventional group symmetry due to
the paramount importance of group symmetry in physics. This led to the theory
of symmetry-enriched topological order. Another direction is the boundary
physics of topological phases, both gapless as in the fractional quantum Hall
physics and gapped as in toric code. A more speculative and interesting
direction is the study of Banados-Teitelboim-Zanelli black holes and quantum
gravity in $3d$. The clearly defined physical and mathematical issues require a
far-reaching generalization of anyons and seem to be within reach. In this
short survey, I will first cover the extensions of anyon theory to symmetry
defects and gapped boundaries. Then I will discuss a desired generalization of
anyons to anyon-like objects---the Banados-Teitelboim-Zanelli black holes---in
$3d$ quantum gravity.
