  We discuss the effects of disorder in time-reversal invariant topological
insulators and superconductors in three spatial dimensions. For
three-dimensional topological insulator in symplectic (AII) symmetry class, the
phase diagram in the presence of disorder and a mass term, which drives a
transition between trivial and topological insulator phases, is computed
numerically by the transfer matrix method. The numerics is supplemented by a
field theory analysis (the large-$N_f$ expansion where $N_f$ is the number of
valleys or Dirac cones), from which we obtain the correlation length exponent,
and several anomalous dimensions at a non-trivial critical point separating a
metallic phase and a Dirac semi-metal. A similar field theory approach is
developed for disorder-driven transitions in symmetry class AIII, CI, and DIII.
For these three symmetry classes, where topological superconductors are
characterized by integer topological invariant, a complementary description is
given in terms of the non-linear sigma model supplemented with a topological
term which is a three-dimensional analogue of the Pruisken term in the integer
quantum Hall effect.
