  Disorder inevitably exists in realistic samples, manifesting itself in
various exotic properties for the topological states. In this paper, we
summarize and briefly review work completed over the last few years, including
our own, regarding recent developments in several topics about disorder effects
in topological states. For weak disorder, the robustness of topological states
is demonstrated, especially for both quantum spin Hall states with $Z_2=1$ and
size induced nontrivial topological insulators with $Z_2=0$. For moderate
disorder, by increasing the randomness of both the impurity distribution and
the impurity induced potential, the topological insulator states can be created
from normal metallic or insulating states. These phenomena and their mechanisms
are summarized. For strong disorder, the disorder causes a metal-insulator
transition. Due to their topological nature, the phase diagrams are much richer
in topological state systems. Finally, the trends in these areas of disorder
research are discussed.
