  The topological model for quantum computation is an inherently fault-tolerant
model built on anyons in topological phases of matter. A key role is played by
the braid group, and in this survey we focus on a selection of ways that the
mathematical study of braids is crucial for the theory. We provide some brief
historical context as well, emphasizing ways that braiding appears in physical
contexts.
  We also briefly discuss the 3-dimensional generalization of braiding: motions
of knots.
