  In the three-dimensional topological insulator (TI), the physics of doped
semiconductors exists literally side-by-side with the physics of
ultra-relativistic Dirac fermions. This unusual pairing creates a novel
playground for studying the interplay between disorder and electronic
transport. In this mini-review we focus on the disorder caused by the
three-dimensionally distributed charged impurities that are ubiquitous in TIs,
and we outline the effects it has on both the bulk and surface transport in
TIs. We present self-consistent theories for Coulomb screening both in the bulk
and at the surface, discuss the magnitude of the disorder potential in each
case, and present results for the conductivity. In the bulk, where the band gap
leads to thermally activated transport, we show how disorder leads to a
smaller-than-expected activation energy that gives way to VRH at low
temperatures. We confirm this enhanced conductivity with numerical simulations
that also allow us to explore different degrees of impurity compensation. For
the surface, where the TI has gapless Dirac modes, we present a theory of
disorder and screening of deep impurities, and we calculate the corresponding
zero-temperature conductivity. We also comment on the growth of the disorder
potential as one moves from the surface of the TI into the bulk. Finally, we
discuss how the presence of a gap at the Dirac point, introduced by some source
of time-reversal symmetry breaking, affects the disorder potential at the
surface and the mid-gap density of states.
